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.
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.
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.
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