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 М₁ М₂;

6. determine a relative position of straight lines М₁ М₂ 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.

 

1.	11.	21.
2.	12.	22.
3.	13.	23.
4.	14.	24.
5.	15.	25.
6.	16.	26.
7.	17.	27.
8.	18.	28.
9.	19.	29.
10.	20.	30.

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