Тема 2. Геометрические задачи на прямую на плоскости.

338. а) 90; б) arccos 339. а); б) 340. M(0; 3),  = arccos = arctg 2

341. 342.  343. 3x - 2y - 7 = 0 344. 4x + y + 5 = 0, y - 3 = 0

345. x - 5y + 3 = 0, 5x + y - 11 = 0 346. 2x - y - 6 = 0, 2x + y - 6 = 0 347. 1; ;

348. 349. О(0; 1), r = 350. О(1; 0), R = 351. M(10; 21) 352. S = 9

353. x + y - 7 = 0 354. 2x + 3y - 12 = 0 355. 3x + 2y - 6 = 0, 3x + 8y + 12 = 0

356. M₁ (2; 5), M₂ (14; 17) 357. M₁ (-3; 12), M₂ (1; 5), M₃ (- ; ); ‖

Дополнительные задачи.

358. [AB], [AC]: 2x + 7y + 22 = 0, 7x + 2y - 13 = 0; [BC]: x - y + 2 = 0.

359. [AB], [AC]: x - 3y + 10 = 0, x + 4y - 4 = 0; [BC]: 2x + y - 8 = 0.

360. [AB], [AC]: x - y - 6 = 0, 7x + y - 10 = 0; [BC]: x + 7y - 6 = 0.

361. [AB], [AC]: 4x - 3y + 10 = 0, 7x + y - 20 = 0; [BC]: 3x + 4y - 5 = 0.

362. [AB], [AC]: x - 3y - 23 = 0, 4x + 3y + 13 = 0; [BC]: 7x + 9y + 19 = 0.

363. [AB], [AC]: 6x - 7y - 25 = 0, 18x + 13y - 41 = 0; [BC]: 2x + 9y - 65 = 0.

Тема 3. Кривые 2-го порядка

.

364. а) C (4; -3), R = 2; б) C (2; 0), R = 2; в) C (0; -3), R = 4; г) C (; - ), R = 1

365. (x + 3)² + (y + 2)² = 25 366. x² + (y - 2)² = 4 367. (x - 2)² + (y + 3)² = 4 и (x + 2)² + (y + 3)² = 4

368. (x - 5)² + (y - 5)² = 25 и (x - 17)² + (y - 17)² = 289 369. (x - 6)² + (y - 7)² = 36

370. x - 2y - 5 = 0 371. 4x + 3y - 35 = 0 372. 2x - 3y + 9 = 0 373. 60

374. d = 4 375. (x - )² + (y - )² = и (x - )² + (y - )² =

.

376. a = 5, b = 3; F₁(-4; 0), F₂(4; 0); e = 0,8; d = 12,5; D₁: x + 6,25 = 0; D₂: x - 6,25 = 0

377. а) + = 1; б) + = 1; в) + = 1; г) + = 1; д) + = 1; е) + = 1

378. а) C(3; -1); a = 3, b = ; F₁(1; -1), F₂(5; -1); e = ; d = 9; D₁: 2x + 3 = 0; D₂: 2x - 15 = 0

б) C(-1; 2); a = 5, b = 4; F₁(-4; 2), F₂(2; 2); e = 0,6; d = 16; D₁: 3x + 28 = 0; D₂: 3x - 22 = 0

в) C(1; -2); a = 2, b = 4; F₁(1; -4), F₂(1; 0); e = 0,5; d = 16; D₁: y + 10 = 0; D₂: y - 6 = 0

379. а) e = ; б) e = ; в) e = 0,5 380. M₁(-7,5; - ), M₂(-7,5; ) 381.

382. x2y 8 = 0 383. y 3 = 0 и 12x 7y 51 = 0 384. 2x y  12 = 0 385. 12x 13y  169 = 0

.

386. a = 3, b = 4; F₁(-5; 0), F₂(5; 0); e = ; d = 3,6; k =  ; L₁ , L₂ : y =  x; D₁: 5x + 9 = 0; D₂: 5x - 9 = 0

387. а) = 1; б) = 1; в) = 1; г) = 1; д) = 1; а) = 1

388. а) C(2; -3); a = 3, b = 4; F₁(-3; -3), F₂(7; -3); e = ; d = 3,6; L₁ , L₂: 4x 3y 17 = 0, 4x 3y 1 = 0, D₁: 5x 1 = 0; D₂: 5x 19 = 0

б) C(-5; 1); a = 8, b = 6; F₁(-15; 1), F₂(5; 1); e = ; d = 12,8; L₁ , L₂: 3x 4y 19 = 0, 3x 4y 11 = 0, D₁: 5x 57 = 0; D₂: 5x 7= 0

в) C(2; -1); a = 3, b =4; F₁(2; -6), F₂(2; 4); e = ; d = 6,4; L₁ , L₂: 4x 3y 11 = 0, 4x 3y 5 = 0, D₁: 5 y 21 = 0; D₂: 5 y 11 = 0

389. а) e = или e = 2; б) e = ; в) e = 390. 90 391. M₁(9,6; - ), M₂(9,6; )

392. x y 1 = 0 393. 3x 2y 6 = 0 и 3x 2y 6 = 0 394. x y  3 = 0 395. 2x y  3 = 0

.

396. а) p = 3, l = OX, F(1,5; 0); D: 2x 3 = 0 б) p = 0,5, l = OY, F(0; -0,25); D: 4y 1 = 0 в) p = 2, l = OX, F(-1; 0); D: x 1 = 0 г) p = 2,5, l = OY, F(0; 1,25); D: 4y 5 = 0

397. а) y² = - x б) x² = - 2y в) x² = - 12y

398. а) C(2; 0); p = 2, l = OX, F(3; 0); D: x 1 = 0 б) C(0; 2); p = 0,5, l = OY, F(0; 1,75); D: 4y 9 = 0 в) C(1; 3); p = , l: x 1 = 0, F(1; 3); D: 16y 47= 0 г) C(1; 2); p = 2, l: y2 = 0, F(0; 2); D: x2 = 0

399. 10 400. 2p 401. x y 2 = 0 и 2x 5y 25 = 0 402. 3x y 1 = 0 403. x 2y 12 = 0

Дополнительные задачи.

404. M₀(-3; 2), d = 405. M₀(-6; 3), d = 406. M₀(9; -24), d = 4

407. 2x 11y 10 = 0 408. 2x 11y 6 = 0 409. y 18 = 0