Добавил:

ivanov666 Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Пермский Государственный аграрно-технологический университет им. Д.Н. Прянишникова

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

821

.pdf

Скачиваний:

Добавлен:

09.01.2024

Размер:

5.5 Mб

Скачать

☆

<<< < Предыдущая 1 2 3 4 5 6 7 8 9 10 1112 / 3112 13 14 15 16 17 18 19 20 21 22 23 24 25 > Следующая >>>

3) 872 + 162 = 1;

147

5)( −175 )2 + ( +92)2 = 1; 16 4

2.20.1) 1212 + 162 = 1;

3)182 + 52 = 1;

		7						6						2
											15			2
	5)	2	+				( −				8 )				= 1;
	5)	81	+												= 1;
		81						16
2.21.	1)	2			+			2			= 1;
2.21.	1)	100			+			9			= 1;
		100						9
	3)	2		+				2			= 1;
	3)	19		+				10			= 1;
		5			9			27						6		2
		( +				)							( + )
		( +				)							( + )
	5)				10				+					5			= 1;
	5)	121							+					81			= 1;
		121												81
2.22.	1)	2			+			2			= 1;
2.22.	1)	225			+			81			= 1;
		225						81
	3)	2		+ 2 = 1;
	3)	27		+ 2 = 1;
		16				2
					8	2
	5)	( +3)						+				2		= 1;
	5)	121						+			64			= 1;
		121									64
2.23.	1)	2	+				2			= 1;
2.23.	1)	49	+			16				= 1;
		49				16
	3)	2		+				2			= 1;
	3)	28		+				11			= 1;
		15			16			29						5		2
		( +			7	)							( − )
	5)				7				+					3			= 1;
	5)	169							+					121			= 1;
		169												121

2.24.1) 1002 + 812 = 1;

3)142 + 142 = 1;

1925

5)( −138 )2 + ( +185 )2 = 1; 121 49

2.25.1) 252 + 92 = 1;

3)72 + 152 = 1;

	3				11							2
										15		2
5)	2		+			( −				4 )			= 1;
5)	169		+		100								= 1;
	169				100
2.26. 1)	2		+			2		= 1;
2.26. 1)	100		+		36			= 1;
	100				36
3)	2	+			2				= 1;
3)	18	+			10				= 1;
	5		8		29								13		2
	( −			)							( +		7	)
	( −			)							( +			)
5)			11				+									= 1;
5)	36						+					25				= 1;
	36											25

111

4)	2	+			( −8)2										= 1;
4)	64	+													= 1;
	64							49
	( −			7		)2												1 2
	( −					)2												1 2
6)		13								+				( +									) = 1.
6)		25								+				( +							2		) = 1.
	2	16			2
2)		+								= 1;
2)	54	+			20					= 1;
	54				20
4)	( +8)2							+					( −2)2					= 1;
4)	64							+										= 1;
	64													25
	( +8)2																	2
6)		5							+ ( +										15					)			= 1.
6)		16							+ ( +															)			= 1.
		9																2
	2	9			2
2)		+								= 1;
2)	56	+			12					= 1;
	56				12
4)	2	+			( −3)2										= 1;
4)	36	+													= 1;
	36							4
					15						2						( +7)2
6) ( +										)				+				3										= 1.
6) ( +							2			)				+				4										= 1.
	2				2													9
2)	2	+			2					= 1;
2)	63	+			40					= 1;
	63				40
4)	( +9)2							+				( +9)2						= 1;
4)	49							+										= 1;
	49													36
					18						2						( +6)2
6) ( −										)				+				5										= 1.
6) ( −							11			)				+						9								= 1.
	2						11											16
																		16
2)			+ 2 = 1;
2)	32		+ 2 = 1;
4)	( −4)2							+					( +1)2					= 1;
4)								+										= 1;
	81													25
	2										2				2
	2							( + )
6)			+								9					= 1.
6)	16		+								1					= 1.
	25										4
2)	2	+			2					= 1;
2)	94	+			70					= 1;
	94				70
4)	2	+			( +7)2										= 1;
4)	36	+													= 1;
	36							4
					15						2						( −8)2
6) ( +										)				+				3										= 1.
6) ( +							4			)				+						9								= 1.
							4											16
	2				2													16
2)	2	+			2					= 1;
2)	76	+			52					= 1;
	76				52
4)	( −8)2							+					( +2)2					= 1;
4)	121							+										= 1;
	121													49
	( +19)2																	10									2
6)		15								+				( +											) = 1.
6)		9								+				( +							7				) = 1.
	2	4			2
2)		+								= 1;
2)	32	+			15					= 1;
	32				15
4)	( +4)2							+					2		= 1;
4)	225							+			81				= 1;
	225										81
								8			2						( −					6				)2
								8			2						( −									)2
6) ( +										)				+				11											= 1.
6) ( +							15			)				+				16											= 1.
																		49

2.27.1) 1442 + 812 = 1;

3)2 = 1;48 + 2

		25						2												2
		( +				19		2										1		2
		( +					)								( − )
	5)					15					+							5			= 1;
	5)			9							+						4				= 1;
				9													4
2.28.	1)	2		+			2					= 1;
2.28.	1)	49		+			25					= 1;
		49					25
	3)	2			+				2				= 1;
	3)	2			+			13					= 1;
								16
						10 2									2
	5)	( − 7 )									+				2			= 1;
	5)										+			9				= 1;
		36												9
2.29.	1)	2		+			2					= 1;
2.29.	1)	81		+			16					= 1;
		81					16
	3)	2			+			2					= 1;
	3)	1			+					4			= 1;
		2				9	215						( +				11			2
		( + )											( +					3	)
	5)					5			+									3			= 1;
	5)	25							+					4							= 1;
		25												4
2.30.	1)	2		+			2					= 1;
2.30.	1)	49		+			25					= 1;
		49					25
	3)	2		+ 2 = 1;
	3)		8	+ 2 = 1;
		13						2
						14		2
	5)	( − 9 )									+				2			= 1;
	5)										+			81				= 1;
		169												81
2.31.	1)	2		+			2					= 1;
2.31.	1)	36		+			9					= 1;
		36					9
	3)	2			+			2					= 1;
	3)	14			+			14					= 1;
		5				17		29										4		2
		( −					)								( + )
	5)					18					+							3			= 1;
	5)	225									+			100							= 1;
		225												100
2.32.	1)	2		+			2					= 1;
2.32.	1)	64		+			16					= 1;
		64					16
	3)	2 +						2					= 1;
	3)	2 +						3					= 1;
						9	2 8
	5)	( −5)							+				2			= 1;
	5)	36							+							= 1;
		36												4
2.33.	1)		2			+				2				= 1;
2.33.	1)	169				+		144						= 1;
		169						144
	3)	2			+			2					= 1;
	3)	2			+					5			= 1;
		5						18
		( +				12		2										4		2
		( +				7	)								( − )
	5)					7					+							3			= 1;
	5)	25									+						9				= 1;
		25															9
2.34.	1)	2		+			2					= 1;
2.34.	1)	64		+			49					= 1;
		64					49
	3)	2			+			2					= 1;
	3)	14			+			10					= 1;
		3						3

112

2)	2	+		2							= 1;
2)	62	+		44							= 1;
	62			44
4)	( −3)2						+							( +5)2										= 1;
4)	25						+																	= 1;
	25																16
															5				2
	2						( +											)
	2						( +											)
6)		+													14								= 1.
6)	25	+									36												= 1.
	9										49
2)	2	+		2							= 1;
2)	97	+		80							= 1;
	97			80
4)	( +1)2						+							( +2)2										= 1;
4)	169						+																	= 1;
	169																81
		7		2												( −							18	2
	( + )															( −							5	)
6)		3							+														5				= 1.
6)	36								+										25								= 1.
	2 49			2															36
2)		+									= 1;
2)	76	+		21							= 1;
	76			21
4)	2		+					( −3)2												= 1;
4)	121		+																	= 1;
	121										49
	( +12)2																							10					2
6)		5										+ ( −																) = 1.
6)		25										+ ( −														3		) = 1.
	2	9		2
2)		+									= 1;
2)	68	+		23							= 1;
	68			23
4)	( +9)2							+					( −2)2											= 1;
4)	64							+																= 1;
	64																36
															7		2
6)	2	+				( +5)																= 1.
6)	64	+			25																	= 1.
	9										9
2)	2	+		2							= 1;
2)	56	+		19							= 1;
	56			19
4)	2		+					( +5)2												= 1;
4)	121		+																	= 1;
	121										49
							7				2												( +21)2
6) ( −												) +												16							= 1.
6) ( −						13						) +													9						= 1.
						13																		64
	2			2																				64
2)	2	+		2							= 1;
2)	98	+		62							= 1;
	98			62
4)	( +2)2							+						( −7)2										= 1;
4)	100							+																= 1;
	100																81
	( +14)2																							17					2
6)		9										+ ( −																) = 1.
6)		25										+ ( −														4		) = 1.
	2	9		2
2)		+									= 1;
2)	76	+		54							= 1;
	76			54
4)	( −4)2							+						2					= 1;
4)	64							+											= 1;
	64										36
				5							2										( +23)2
6) ( −										) +														17						= 1.
6) ( −						4				) +														16						= 1.
	2			2																				49
2)	2	+		2							= 1;
2)	48	+		34							= 1;
	48			34
4)	2	+		( +1)2															= 1;
4)	81	+					25												= 1;
	81						25

			( +15)2												( +6)2								( −21)2																			8 2
	5)					16					+							5			= 1;	6)					8					+ ( −													)		= 1.
	5)	121									+					100					= 1;	6)		25								+ ( −											3		)		= 1.
			2							2													2	9				2
2.35.	1)					+							= 1;									2)		+								= 1;
2.35.	1)	225				+			81				= 1;									2)	44	+				18				= 1;
		225							81														44					18
	3)		2			+				2			= 1;									4)	( +7)2								+			( −1)2							= 1;
	3)		2			+			12				= 1;									4)	121								+					64					= 1;
									17														121													64
			( +56)2						17					( +125 )2
	5)		( +56)2							+				( +125 )2							= 1;	6)	2		+				( +									9	)2		= 1.
	5)	36								+											= 1;	6)	25		+				( +										)2		= 1.
		36														9							4														2
																							4
2.36.	1)		2		+		2					= 1;										2)	2		+ 2 = 1;
2.36.	1)	36			+		25					= 1;										2)	11		+ 2 = 1;
	3)		2			+		2					= 1;									4)	( −8)2								+			( +2)2							= 1;
	3)		5			+		2					= 1;									4)									+					49					= 1;
		3							3														64													49
		3				7	2		3									23		2			2												10		2
			( + )											( −				8	)				2								( +				7	)
	5)					4				+								8			= 1;	6)			+										7					= 1.
	5)	169								+					100						= 1;	6)	49		+								25							= 1.
																							4										16
		3. Построение эллипса по его каноническому или
																			нормальному уравнению
Задание 3. Построить эллипс по его каноническому или нормально-
му уравнению.
3.1.	1)		2			+				2			= 1;									2)	2	+				2				= 1;
3.1.	1)	225				+			81				= 1;									2)	38	+				20				= 1;
		225							81														38					20
	3)		2			+		2					= 1;									4)	( +4)2								+			( −1)2							= 1;
	3)		91			+		18					= 1;									4)	64								+					36					= 1;
		16							5														64													36
		16							5
			( +14)2													2							( −11)2																			2
	5)					9					+							= 1;				6)		8								+ ( +											11			)	= 1.
	5)	25									+				4			= 1;				6)		100								+ ( +										4				)	= 1.
		25													4									49																		4
			2							2													2	49				2
3.2.	1)					+									= 1;							2)		+								= 1;
3.2.	1)	196				+			100						= 1;							2)	84	+				32				= 1;
		196							100														84					32
	3)		2			+		2					= 1;									4)	( −4)2								+			2			= 1;
	3)		82			+		45					= 1;									4)	25								+				9		= 1;
		17							19														25												9
		17							19
			( +9)2											( −6)2														11					2							( +11)2
	5)					4				+								5		= 1;		6) ( −										) +										4						= 1.
	5)	64								+						36				= 1;		6) ( −								8		) +										16						= 1.
			2				2																2					2														49
3.3.	1)		2		+		2					= 1;										2)	2	+				2				= 1;
3.3.	1)	81			+		36					= 1;										2)	33	+				10				= 1;
		81					36																33					10
	3)		2			+			2				= 1;									4)	( +3)2								+			( −8)2							= 1;
	3)		2			+			19				= 1;									4)	64								+						4				= 1;
									23														64														4
									23
						15			2						2											12					2									8		2
			( −			7	)								2								( −				7	)								( + )
	5)					7					+						= 1;					6)					7					+								3				= 1.
	5)	100									+				49		= 1;					6)		36								+					64							= 1.
			2							2													2	25													81
3.4.	1)		2			+				2			= 1;									2)	2		+ 2 = 1;
3.4.	1)	100				+			49				= 1;									2)	79		+ 2 = 1;
	3)		2			+		2					= 1;									4)	( +1)2								+			( −8)2							= 1;
	3)		60			+		47					= 1;									4)									+						9				= 1;
		13							15														16														9
		13							15							2															2											2
			2				( −						14			2							( +			10					2									6		2
			2				( −						3		)								( +				3	)								( + )
	5)			+									3					= 1;				6)					3					+								5				= 1.
	5)		81	+					49									= 1;				6)		64								+					36							= 1.
			2							2													2	9				2									25
3.5.	1)					+							= 1;									2)		+								= 1;
3.5.	1)	121				+			64				= 1;									2)	34	+				11				= 1;
		121							64														34					11

113

	3)	2		+			2			= 1;
	3)	2		+		60				= 1;
					2	87										2
				5	2						( +		15			2
		( − )									( +		8			)
	5)			2			+						8					= 1;
	5)	81					+					36						= 1;
		81										36
3.6.	1)	2	+		2				= 1;
3.6.	1)	81	+		49				= 1;
		81			49
	3)	2		+ 2 = 1;
	3)	15		+ 2 = 1;
		4				2												2
		( +		18		2						( +		10			)	2
		( +			)							( +			9		)
	5)			13				+							9				= 1;
	5)	121						+				36							= 1;
		121										36
3.7.	1)	2		+			2			= 1;
3.7.	1)	100		+		64				= 1;
		100				64
	3)	2		+		2				= 1;
	3)	21		+		19				= 1;

813

5)( +43)2 + ( −127 )2 = 1; 49 16

3.8.1) 812 + 252 = 1;

3) 2 + 82 = 1;

				11
		10 2						2
5)	( − 7 )				+				= 1;
	100
						49
3.9. 1)	2	+		2		= 1;
	144		81

3)	2	+	2				= 1;
	32		5

174

5)2 + ( +115 )2 = 1; 36 9

3.10.1) 642 + 252 = 1;

3)142 + 72 = 1;

5)( +87)2 + ( +1912)2 = 1; 49 16

3.11.1) 2252 + 1442 = 1;

3) 2 + 32 = 1;

			6	2		10		( +			13	2
	( − )							( +			5	)
5)			5			+					5		= 1;
5)	81					+			25				= 1;
	81								25
3.12. 1)	2		+			2	= 1;
3.12. 1)	100		+			64	= 1;
	100					64
3)	2		+			2	= 1;
3)	7		+			7	= 1;
	4					9			2
							8		2
5)	2	+			( −3)					= 1;
5)	36	+								= 1;
	36					4

114

4)	( +4)2					+		( −1)2						= 1;
4)	196					+			100					= 1;
	196								100
			14			2				2
6)	( −		9	)			+			2			= 1.
			9
		25								81
	2	4		2					100
2)		+					= 1;
2)	57	+		18			= 1;
	57			18
4)	( −3)2					+		( +2)2						= 1;
4)	100					+			64					= 1;
	100								64
								5	2
6)	2	+			( −3)							= 1.
6)	25	+			16							= 1.
	9						49
2)	2	+		2			= 1;
2)	66	+		51			= 1;
	66			51
4)	2		+			( −8)2						= 1;
4)	169		+									= 1;
	169						81
	( −13)2														7			2
6)			8				+ ( +										) = 1.
6)		4					+ ( +									4	) = 1.
	2	9		2
2)		+					= 1;
2)	84	+		75			= 1;
	84			75
4)	( +2)2					+		( −5)2						= 1;
4)	121					+			64					= 1;
	121								64
	( −		15			2							4		2
	( −			)						( + )
6)			11				+						3					= 1.
6)		16					+					16						= 1.
	2	9										25
2)	2	+ 2 = 1;
2)	4	+ 2 = 1;
4)	( −7)2					+		( +2)2						= 1;
4)	196					+			49					= 1;
	196								49
			10			2							15		2
6)	( −		7 )				+			( +			8 )						= 1.
6)		64					+					9							= 1.
	2	25				2						4
2)			+					= 1;
2)	196		+			81		= 1;
	196					81
4)	2		+			( −4)2						= 1;
4)	100		+				36					= 1;
	100						36
	( −11)2														5			2
6)			5				+ ( +										) = 1.
6)		16					+ ( +									4	) = 1.
	2	9		2
2)		+					= 1;
2)	90	+		73			= 1;
	90			73
4)	( +3)2					+		2			= 1;
4)	64					+		16			= 1;
	64							16
			18			2							9		2
	( +			)						( +					)
6)	( +		7	)			+			( +			11		)				= 1.
			7										11
		49										25
	2	16		2								16
2)		+					= 1;
2)	54	+		32			= 1;
	54			32
4)	( −5)2					+		( +2)2						= 1;
4)	169					+			49					= 1;
	169								49
	( +13)2														4			2
6)			8				+ ( +										) = 1.
6)		16					+ ( +									5	) = 1.
		9

3.13.	1)	2	+			2				= 1;
3.13.	1)	16	+			9				= 1;
		16				9
	3)	2	+ 2 = 1;
	3)	18	+ 2 = 1;
		13				2										2
					9	2					( +		16			2
		( − )									( +			7		)
	5)				5			+						7				= 1;
	5)	81						+				25						= 1;
		81										25
3.14.	1)	2	+			2				= 1;
3.14.	1)	64	+			25				= 1;
		64				25
	3)	2		+			2				= 1;
	3)	2		+			10				= 1;
							17
		( −			15	)	2					( −			10		)	2
		( −			7	)						( −			3		)
	5)				7				+						3				= 1;
	5)	144							+			81							= 1;
		144										81
3.15.	1)	2			+			2				= 1;
3.15.	1)	169			+		100					= 1;
		169					100
	3)	2		+			2				= 1;
	3)	7		+			5				= 1;

5)( +139 )2 + ( −85)2 = 1; 64 16

3.16.1) 812 + 642 = 1;

3)102 + 2 = 1;

	7		2					2
		6	2				9	2
	( + )						( − )
5)		5			+		8		= 1;
5)	25				+		9		= 1;
	25						9
3.17. 1)	2	+	2			= 1;
3.17. 1)	25	+	9			= 1;
	25		9
3)	2	+		2			= 1;
3)	8	+		5			= 1;

5)( +154 )2 + 2 = 1; 100 16

3.18.1) 1442 + 812 = 1;

3)2 + 132 = 1;

			10	29								5	2
		( − )								( + )
	5)		7				+					2		= 1;
	5)	49					+					9		= 1;
		49										9
3.19.	1)	2	+		2			= 1;
3.19.	1)	169	+	64				= 1;
		169		64
	3)	2	+ 2 = 1;
	3)	11	+ 2 = 1;
		5									2
								9			2
	5)	2	+			( +7)						= 1;
	5)	100	+					4				= 1;
		100						4
3.20.	1)	2	+			2			= 1;
3.20.	1)	121	+	49					= 1;
		121		49
	3)	2	+ 2 = 1;
	3)	19	+ 2 = 1;
		8

115

2)	2	+			2							= 1;
2)	92	+			50							= 1;
	92				50
4)	( +3)2							+							( −1)2						= 1;
4)	144							+									64				= 1;
	144																64
															7			2
6)	2						+			( +3)										= 1.
6)	100						+		16											= 1.
	81													49
2)	2	+			2							= 1;
2)	80	+			34							= 1;
	80				34
4)	( +8)2							+							( +2)2						= 1;
4)	121							+									49				= 1;
	121																49
				12				2									2
	( +			5	)												2
6)				5									+							= 1.
6)		25											+				64			= 1.
	2	16			2												49
2)		+										= 1;
2)	72	+			26							= 1;
	72				26
4)	2	+			( +9)2													= 1;
4)	81	+						25										= 1;
	81							25
	( −18)2																					10					2
6)				11									+ ( +													) = 1.
6)		9											+ ( +										9			) = 1.
	2	4			2
2)		+										= 1;
2)	50	+			27							= 1;
	50				27
4)	( −8)2							+							( +5)2						= 1;
4)	36							+										4			= 1;
	36																	4
															1		2
6)	2		+				( −2)												= 1.
6)	16		+			100													= 1.
	9											81
2)	2	+			2							= 1;
2)	48	+			20							= 1;
	48				20
4)	( +6)2							+							( −2)2						= 1;
4)	121							+									49				= 1;
	121																49
					2 2														( −			7			)2
					2 2														( −						)2
6) ( −											)				+							13						= 1.
6) ( −							9				)				+						16							= 1.
	2				2																25
2)	2	+			2							= 1;
2)	92	+			40							= 1;
	92				40
4)	( +4)2							+							( +1)2						= 1;
4)	100							+									36				= 1;
	100																36
	( +			14				2									2
	( +			5	)												2
6)				5									+							= 1.
6)		16											+				64			= 1.
	2	9			2												49
2)		+										= 1;
2)	52	+			18							= 1;
	52				18
4)	( −3)2							+							( +5)2						= 1;
4)	49							+									16				= 1;
	49																16
				8	2											( +				16	2
	( + )															( +				3	)
6)				3						+										3				= 1.
6)		81								+									9					= 1.
	2	16			2														4
2)		+										= 1;
2)	28	+			6							= 1;
	28				6
4)	( +1)2							+							( +3)2						= 1;
4)	81							+									25				= 1;
	81																25

		9	2					( +	12	)	2
	( − )							( +	5	)
5)		2				+			5			= 1;
5)	25					+		16				= 1;
	25							16
3.21. 1)	2	+		2			= 1;
3.21. 1)	81	+		16			= 1;
	81			16
3)	2	+			2			= 1;
3)	5	+			2			= 1;

5)( +178 )2 + ( +103 )2 = 1; 100 49

3.22.1) 1962 + 1212 = 1;

3) 2 + 12 = 1;

		6	2 2				( +	11	)	2
	( + )						( +		)
5)		5			+			7			= 1;
5)	25				+		4				= 1;
	25						4
3.23. 1)	2	+	2			= 1;
3.23. 1)	25	+	4			= 1;
	25		4
3)	2	+		2			= 1;
3)	11	+		11			= 1;

5)2 + ( −154 )2 = 1; 49 25

3.24.1) 492 + 162 = 1;

3)182 + 2 = 1;

		13			2										2
				9	2						( −		14	)	2
		( − )									( −		5	)
	5)			5			+						5			= 1;
	5)	64					+			36						= 1;
		64								36
3.25.	1)	2		+			2			= 1;
3.25.	1)	196		+		81				= 1;
		196				81
	3)	2 +				2				= 1;
	3)	2 +				5				= 1;
				17 29
	5)	( + 3 )						+				2	= 1;
	5)	121						+					= 1;
		121								64
3.26.	1)	2	+		2				= 1;
3.26.	1)	16	+		9				= 1;
		16			9
	3)	2		+		2				= 1;
	3)	15		+		10				= 1;
		7		8	2	3					( +		15	)	2
		( + )									( +		2	)
	5)			5			+						2			= 1;
	5)	64					+			25						= 1;
		64								25

3.27.1) 1962 + 812 = 1;

3) 2 + 172 = 1;

		10	25				10	2
5)	( −	3 )			+		( + 7 )		= 1;
5)	9				+		4		= 1;
	9						4
3.28. 1)	2	+		2		= 1;
3.28. 1)	100	+		49		= 1;
	100			49

116

															3			2
6)	2					+				( −2)											= 1.
6)	100					+			100												= 1.
	81													49
2)	2		+		2							= 1;
2)	50		+		18							= 1;
	50				18
4)	( −8)2						+								2			= 1;
4)	64						+								25			= 1;
	64														25
							4								2						( −5)2
6) ( −													) +									7								= 1.
6) ( −						15							) +											9						= 1.
						15																25
	2				2																	25
2)	2		+		2							= 1;
2)	72		+		51							= 1;
	72				51
4)	( −5)2						+								( +1)2							= 1;
4)	81						+								16							= 1;
	81														16
				19			2										2
	( −				)												2
6)				11								+									= 1.
6)			81									+					16				= 1.
	2		25		2										25
2)			+									= 1;
2)	90		+		63							= 1;
	90				63
4)	( +9)2						+								( −6)2							= 1;
4)	144						+								100							= 1;
	144														100
	( +7)2																						12				2
6)	8										+ ( +												12			)				= 1.
6)	121										+ ( +											5				)				= 1.
	2 36																					5
	2 36				2
2)			+									= 1;
2)	85		+		48							= 1;
	85				48
4)	2			+				( +4)2												= 1;
4)	121			+								64								= 1;
	121											64
																			) 2 +			9				2
6) ( −						1														( +7)									= 1.
6) ( −																				16									= 1.
					4																25
	2				2																25
2)	2		+		2							= 1;
2)	70		+		32							= 1;
	70				32
4)	( −2)2						+								( +4)2							= 1;
4)	49						+								16							= 1;
	49														16
				7	2											( +					12	2
	( − )															( +					11	)
6)				5						+											11						= 1.
6)		81								+										49							= 1.
	2100				2													100
2)			+									= 1;
2)	82		+		60							= 1;
	82				60
4)	2			+			( −6)2													= 1;
4)	196			+								121								= 1;
	196											121
	( −19)2																										2
6)	18												+ ( +												11			)		= 1.
6)	225												+ ( +															)		= 1.
			49																			5
	2		49		2
2)			+									= 1;
2)	28		+		12							= 1;
	28				12
4)	( +5)2						+								( −3)2							= 1;
4)	64						+								16							= 1;
	64														16
				15			2										2
6)	( +			4	)							+					2				= 1.
				4
			81														9

254

2)82 + 2 = 1;

3) 122 + 52 = 1;

5)( +1911)2 + ( +83)2 = 1; 36 16

3.29.1) 642 + 252 = 1;

3)172 + 2 = 1;

		5												2
											15			2
	5)	2	+			( +14)									= 1;
	5)	36	+												= 1;
		36								9
3.30.	1)	2		+				2			= 1;
3.30.	1)	196		+			81				= 1;
		196					81
	3)	2		+ 2 = 1;
	3)	14		+ 2 = 1;
		9			2											2
				7	2										9	2
		( + )										( + )
	5)			2				+							4		= 1;
	5)	100						+						25			= 1;
		100												25
3.31.	1)	2	+			2				= 1;
3.31.	1)	81	+		49					= 1;
		81			49
	3)	2		+			2				= 1;
	3)	2		+			13				= 1;
							18
				10 2									2
	5)	( + 3 )							+				2		= 1;
	5)	64							+						= 1;
		64									36
3.32.	1)	2		+				2			= 1;
3.32.	1)	196		+			81				= 1;
		196					81
	3)	2		+			2				= 1;
	3)	15		+			15				= 1;
		4		9	2		7					( +			16	)	2
		( + )										( +			5	)
	5)			4				+							5			= 1;
	5)	49						+						36				= 1;
		49												36

3.33.1) 1442 + 682 = 1;

3)142 + 182 = 1;

917

5)2 + ( −134 )2 = 1; 100 49

3.34.1) 1002 + 92 = 1;

3)2 + 152 = 1;

13 27

5) ( − 9 ) + 2 = 1; 16 4

3.35. 1) 1962 + 642 = 1;

3) 192 + 2 = 1;

5) ( +178 )2 + ( +75)2 = 1; 36 9

117

4) ( 196−7)2 + ( −2)64 2 = 1;

	2							( +						14			2
	2							( +						5		)
6)				+										5							= 1.
6)	144			+							25										= 1.
	49										16
2)	2	+				2			= 1;
2)	99	+				60			= 1;
	99					60
4)	( −1)2						+					( +5)2										= 1;
4)	100						+							49								= 1;
	100													49
					4	2								( −					10			2
	( + )													( −					7			)
6)					5			+											7							= 1.
6)		81						+										9								= 1.
	2	16				2											16
2)		+							= 1;
2)	63	+				45			= 1;
	63					45
4)	2	+				( +7)2										= 1;
4)	36	+					16									= 1;
	36						16
					11		2								2
	( −				3	)									2
6)					3					+									= 1.
6)		16								+					64				= 1.
	2	9				2								49
2)		+							= 1;
2)	56	+				27			= 1;
	56					27
4)	( −8)2						+					( +8)2										= 1;
4)	225						+							121								= 1;
	225													121
					4	2													2			2
	( + )													( − )
6)		7						+									7								= 1.
6)		81						+									25								= 1.
	2100					2											36
2)		+							= 1;
2)	46	+				32			= 1;
	46					32
4)	2	+				( −6)2										= 1;
4)	64	+					36									= 1;
	64						36
	( −2)2																								2
6)		3						+ ( +															5				)	= 1.
6)		25						+ ( +														11					)	= 1.
		9																				11
	2	9				2
2)		+							= 1;
2)	75	+				51			= 1;
	75					51
4)	( +2)2						+					( −5)2										= 1;
4)	25						+									4						= 1;
	25															4
					11		2
6)	( −				8 )					+							2			= 1.
6)		64								+										= 1.
	2	49				2
2)		+							= 1;
2)	28	+				12			= 1;
	28					12
4)	( +7)2						+					( −4)2										= 1;
4)	144						+							81								= 1;
	144													81
	( −1)2																					3 2
6)					2			+ ( +																) = 1.
6)		9						+ ( +															8	) = 1.
	2	4				2
2)		+							= 1;
2)	45	+				20			= 1;
	45					20
4)	( −2)2						+					( +3)2										= 1;
4)	25						+							16								= 1;
	25													16
	2						( −						15			)	2
6)	2		+				( −						16			)				= 1.
6)	49		+								49									= 1.
	4										25

3.36. 1)	2		+	2		= 1;			2)	2	+	2			= 1;
3.36. 1)	81		+	36		= 1;			2)	92	+	68			= 1;
	81			36						92		68
3)	2		+		2		= 1;		4)	( +6)2			+			( +4)2	= 1;
3)	15		+		10		= 1;		4)	100			+			49	= 1;
	7			9						100						49
	7			9
		2		( −5)2						( +9)2							2
5)			+			3		= 1;	6)		4			+ ( −				11	)	= 1.
5)	16		+	9				= 1;	6)		64			+ ( −			4		)	= 1.
	16			9							9						4
											9

4. Определение основных характеристик эллипса по его каноническому уравнению

Задание 4. Дано каноническое уравнение эллипса. Найти: 1) полуоси; 2) фокусы; 3) эксцентриситет; 4) уравнения директрис.


4.1.	2		+		2		= 1.		4.2.	2		+			2		= 1.			4.3.	2		+		2		= 1.
	75				24					40				18							28				9

4.4.	2		+		2		= 1.		4.5.	2		+			2		= 1.			4.6.	2		+		2		= 1.
	32				20					64				54							63				25

4.7.	2		+		2		= 1.		4.8.	2		+			2		= 1.			4.9.	2		+		2		= 1.
	56				36					72				24							49				32

4.10.		2		+		2		= 1.	4.11.		2		+			2		= 1.		4.12.		2		+		2		= 1.
		68				56					45					36						20				8

4.13.		2		+		2		= 1.	4.14.		2		+			2		= 1.		4.15.		2		+		2		= 1.
		34				16					50					9						90				64

4.16.		2		+		2		= 1.	4.17.		2		+			2		= 1.		4.18.		2		+		2		= 1.
		49				24					21					4						76				40

4.19.		2		+		2		= 1.	4.20.		2		+			2		= 1.		4.21.		2		+		2		= 1.
		25				12					75					49						63				36

4.22.		2		+		2		= 1.	4.23.		2		+			2		= 1.		4.24.		2		+		2		= 1.
		32				16					52					9						81				56

4.25.		2		+		2		= 1.	4.26.		2		+			2		= 1.		4.27.		2		+		2		= 1.
		50				28					44					8						64				20

4.28.		2		+		2		= 1.	4.29.		2		+			2		= 1.		4.30.		2		+		2		= 1.
		96				64					63					36						32				12

4.31.		2		+		2		= 1.	4.32.		2			+			2		= 1.	4.33.		2		+		2		= 1.
		80				16					100						52					48				18

4.34.		2		+		2		= 1.	4.35.		2		+			2		= 1.		4.36.		2		+		2		= 1.
		32				9					56					16						72				50

5. Расположение точки относительно эллипса Задание 5. Определить, какие из точек 1, 2, 3, 4 лежат на эллип-

се, какие внутри и какие вне эллипса.

5.1.1(4; −1), 2(−5; 0), 3(√10; 9), 4(−6; 3), 5 2 + 2 2 = 198.

5.2.1(0; 7), 2(−2; −4), 3(−8; 1), 4(5; √6), 3 2 + 7 2 = 199.

5.3.1(−2; 3), 2(1; 4), 3(0; 2), 4(−√3; √7), 4 2 + 7 2 = 79.

5.4.1(3; √7), 2(5; 0), 3(−4; 2), 4(1; 3), 2 + 3 2 = 28.

5.5.1(6; 1), 2(0; 4), 3(−2; −3), 4(√26; 3), 3 2 + 5 2 = 113.

5.6.1(−2; −1), 2(1; 4), 3(3; 0), 4(√2; 4), 8 2 + 3 2 = 56.

5.7.1(√6; 2), 2(0; 4), 3(2; −√3), 4(−3; 1), 9 2 + 5 2 = 74.

5.8.1(−3; 1), 2(−√21; 0), 3(4; −√2), 4(2; 3), 2 2 + 5 2 = 42.

5.9.1(0; 5), 2(3; −4), 3(−2; 4), 4(√15; 2), 5 2 + 3 2 = 87.

5.10.1(√13; 1), 2(1; 4), 3(2; 5), 4(−3; 0), 7 2 + 2 2 = 78.

118

5.11.1(0; 5), 2(2√3; √11), 3(2; 4), 4(3; 4), 4 2 + 5 2 = 103.

5.12.1(2√6; 3), 2(5; −3), 3(0; 5), 4(4; 2), 2 2 + 3 2 = 75.

5.13.1(3; −1), 2(√6; 2), 3(0; 4), 4(−2; √10), 6 2 + 7 2 = 94.

5.14.1(9; √5), 2(−2; 4), 3(−11; 0), 4(3; 6), 2 + 4 2 = 101.

5.15.1(5; −1), 2(√13; 2), 3(−4; 0), 4(√2; 3), 3 2 + 5 2 = 59.

5.16.1(2; −1), 2(1; √7), 3(−3; 0), 4(√3; 2), 4 2 + 3 2 = 24.

5.17.1(2√6; 1), 2(−2; −9), 3(4; 7), 4(0; −11), 5 2 + 2 = 121.

5.18.1(0; 3√2), 2(−1; 4), 3(2√2; −2), 4(3; −3), 7 2 + 4 2 = 72.

5.19.1(−4; 1), 2(3; 0), 3(2; −3), 4(√10; −2), 3 2 + 2 2 = 38.

5.20.1(5; 2), 2(√6; −3), 3(7; 0), 4(−6; 1), 2 + 6 2 = 49.

5.21.1(6; 0), 2(−3; −2), 3(1; 5), 4(−4; 2√3), 4 2 + 5 2 = 124.

5.22.1(−√3; 4), 2(2; 3), 3(0; −√23), 4(−1; 5), 7 2 + 3 2 = 69.

5.23.1(−4; 4), 2(2√3; 6), 3(0; −7), 4(2√5; 2), 3 2 + 2 = 64.

5.24.1(√23; 0), 2(2√2; −5), 3(−3; 4), 4(1; 7), 5 2 + 3 2 = 115.

5.25.1(−7; 1), 2(2√2; −3), 3(0; 4), 4(−6; 2), 2 2 + 5 2 = 92.

5.26.1(0; −4), 2(3√2; 1), 3(−1; 3), 4(√6; −2), 4 2 + 3 2 = 48.

5.27.1(√2; −4), 2(−1; 2√5), 3(2; 2), 4(3; 0), 8 2 + 3 2 = 68.

5.28.1(−2; −3√2), 2(3; 4), 3(5; 6), 4(0; −√19), 2 + 4 2 = 76.

5.29.1(5; 1), 2(−3; 2√3), 3(−2; √14), 4(0; 4), 3 2 + 5 2 = 82.

5.30.1(−√7; 0), 2(2; 5), 3(1; 3√3), 4(−1; 6), 6 2 + 2 = 42.

5.31.1(√10; 1), 2(−1; 2√2), 3(0; −3), 4(2; 4), 4 2 + 5 2 = 45.

5.32.1(0; 5), 2(1; −2√5), 3(−2; 4), 4(2; 3), 7 2 + 3 2 = 67.

5.33.1(−1; 4), 2(3; 0), 3(−√6; 1), 4(2; √7), 5 2 + 2 2 = 37.

5.34.1(0; √6), 2(−5; 3), 3(3; 2√3), 4(7; −1), 2 + 6 2 = 55.

5.35.1(2; √7), 2(−4; 1), 3(−√10; −2), 4(0; 3), 3 2 + 7 2 = 58.

5.36.1(−3√3; √2), 2(5; −1), 3(2; 4), 4(4√2; 0), 2 2 + 5 2 = 64.

6. Составление уравнения касательной к эллипсу в его точке Задание 6. Составить уравнение касательной к эллипсу в его точке .

6.1.(8; −4), 1282 + 322 = 1.

6.2.(−4√2; √10), 642 + 202 = 1.

6.3.(6; −5), 722 + 502 = 1.

6.4.(5√2; 6), 1002 + 722 = 1.

6.5.(−5; 3), 502 + 182 = 1.

6.6.(−6; −5), 722 + 502 = 1.

6.7.(3; −2), 182 + 82 = 1.

119

6.8.(7; 5), 982 + 502 = 1.

6.9.(−4; −5), 962 + 302 = 1.

6.10.(−5√2; 2), 602 + 242 = 1.

6.11.(4; −3), 642 + 122 = 1.

6.12.(−5; −6), 1002 + 482 = 1.

6.13.(5; −4), 752 + 242 = 1.

6.14.(−6; 2), 1082 + 62 = 1.

6.15.(4; −2), 482 + 62 = 1.

6.16.(3; 5), 542 + 302 = 1.

6.17.(−3√2; 2√3), 722 + 162 = 1.

6.18.(4; −3), 322 + 182 = 1.

6.19.(8; −5), 1282 + 502 = 1.

6.20.(−7; 2√3), 982 + 242 = 1.

6.21.(−4; −6), 642 + 482 = 1.

6.22.(3; −3), 362 + 122 = 1.

6.23.(−5; 3), 1002 + 122 = 1.

6.24.(4; 5√2), 962 + 602 = 1.

6.25.(5; −2), 502 + 82 = 1.

6.26.(−4; 3), 322 + 182 = 1.

6.27.(−8; −5√2), 1282 + 1002 = 1.

6.28.(−4; −2√3), 322 + 242 = 1.

6.29.(5; −3), 502 + 182 = 1.

6.30.(−5; 4), 502 + 322 = 1.

6.31.(−3√2; 3), 722 + 122 = 1.

6.32.(5; −2), 752 + 62 = 1.

6.33.(4; 2), 482 + 62 = 1.

6.34.(−5; −4), 502 + 322 = 1.

6.35.(−6; 4), 722 + 322 = 1.

6.36.(8; −√10), 1282 + 202 = 1.

120

<<< < Предыдущая 1 2 3 4 5 6 7 8 9 10 1112 / 3112 13 14 15 16 17 18 19 20 21 22 23 24 25 > Следующая >>>

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]

#
09.01.20245.44 Mб0817.pdf
#
09.01.20245.44 Mб0818.pdf
#
09.01.20245.46 Mб0819.pdf
#
09.01.2024441.6 Кб082.pdf
#
09.01.20245.47 Mб0820.pdf
#
09.01.20245.5 Mб2821.pdf
#
09.01.20245.54 Mб0822.pdf
#
09.01.20245.55 Mб1823.pdf
#
09.01.20245.55 Mб0824.pdf
#
09.01.20245.55 Mб0825.pdf
#
09.01.20245.57 Mб0826.pdf