| 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.
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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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| 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
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Date: 2015-01-02; view: 1082
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