Tsis 2. Analytic geometry in the plane.
Problem 1. Coordinates of points М1, М2 and the equation of straight line d are given. It is required:
1. Construct a straight line d and points М1 and М2;
2. Calculate the distance from the point М1 to the straight line d;
3. Write the equation of the straight line passing through the point М1, parallel to the straight line d;
4. Write the equation of the straight line passing through the point М2 is perpendicular to straight line d;
5. Write the equation of the straight line passing through the points М1 and М2;
6. Determine a relative position of straight lines М1М2 and d; if they are not parallel, to determine the tangent of the angle between them and find the coordinates of the point of their intersection.
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30.
Problem 2. The equation of a curve of the second order is given. Find lengths of half-axles, coordinates of focuses, eccentricity, the equations of asymptotes (for hyperbole). Construct this curve.
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11.
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21.
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12.
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23.
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28.
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Problem 3. Constitute a canonical equation of the parabola whose vertex is at the origin, if it passes through point M and symmetric given axis. Find the coordinates of the focus and the equation of the directrix. Construct this parabola.
1. М(2,2), axis ОХ |
16. М(2,2), axis ОУ |
2. М(5,-3), axis ОХ |
17. М(1,-3), axis ОУ |
3. М(-1,-2), axis ОХ |
18. М(-2,-2), axis ОУ |
4. М(3,-3), axis ОХ |
19. М(2,-3), axis ОУ |
5. М(2,3), axis ОХ |
20. М(-4,3), axis ОУ |
6. М(-2,-1), axis ОХ |
21. М(-1,-1), axis ОУ |
7. М(1,1), axis ОХ |
22. М(-2,1), axis ОУ |
8. М(-2,-2), axis ОХ |
23. М(-1,-2), axis ОУ |
9. М(-4,6), axis ОХ |
24. М(-2,3), axis ОУ |
10. М(3,-5), axis ОХ |
25. М(-3,-1), axis ОУ |
11. М(1,4), axis ОХ |
26. М(-1,-2), axis ОУ |
12. М(-2,3), axis ОХ |
27. М(3,2), axis ОУ |
13. М(-4,-2), axis ОХ |
28. М(-3,-4), axis ОУ |
14. М(-4,5), axis ОХ |
29. М(4,-3), axis ОУ |
15. М(1,-3), axis ОХ |
30. М(1,2), axis ОУ |