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Analytic geometry in the plane.

Problem 1. Coordinates of points Ì1, Ì2 and the equation of straight line d are given. It is required:

1. construct a straight line d and points Ì1 and Ì2;

2. Calculate the distance from the point Ì1 to the straight line d;

3. Write the equation of the straight line passing through the point Ì1, parallel to the straight line d;

4. write the equation of the straight line passing through the point Ì2 is perpendicular to straight line d;

5. write the equation of the straight line Ì1 Ì2;

6. determine a relative position of straight lines Ì1 Ì2 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.

 

1.

2.

3.

4.

5.

6.

7.

8.

9.

10 .

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

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. Ì(2,2), axis ÎÕ 16. Ì(2,2), axis ÎÓ
2. Ì(5,-3), axis ÎÕ 17. Ì(1,-3), axis ÎÓ
3. Ì(-1,-2), axis ÎÕ 18. Ì(-2,-2), axis ÎÓ
4. Ì(3,-3), axis ÎÕ 19. Ì(2,-3), axis ÎÓ
5. Ì(2,3), axis ÎÕ 20. Ì(-4,3), axis ÎÓ
6. Ì(-2,-1), axis ÎÕ 21. Ì(-1,-1), axis ÎÓ
7. Ì(1,1), axis ÎÕ 22. Ì(-2,1), axis ÎÓ
8. Ì(-2,-2), axis ÎÕ 23. Ì(-1,-2), axis ÎÓ
9. Ì(-4,6), axis ÎÕ 24. Ì(-2,3), axis ÎÓ
10. Ì(3,-5), axis ÎÕ 25. Ì(-3,-1), axis ÎÓ
11. Ì(1,4), axis ÎÕ 26. Ì(-1,-2), axis ÎÓ
12. Ì(-2,3), axis ÎÕ 27. Ì(3,2), axis ÎÓ
13. Ì(-4,-2), axis ÎÕ 28. Ì(-3,-4), axis ÎÓ
14. Ì(-4,5), axis ÎÕ 29. Ì(4,-3), axis ÎÓ
15. Ì(1,-3), axis ÎÕ 30. Ì(1,2), axis ÎÓ

Date: 2015-01-02; view: 1033


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