1124 APPENDIX A Polar Form of Conic Sections Appendix A Exercises Graph each conic whose equation is given in polar form. See Example 1. 1. r = 6 3 + 3 sin u 2. r = 9 3 - 3 sin u 3. r = -4 6 + 2 cos u 4. r = -8 4 + 2 cos u 5. r = 2 2 - 4 sin u 6. r = 6 2 - 4 sin u 7. r = -1 1 + 2 cos u 8. r = -1 1 - 2 cos u 9. r = 1 2 + cos u 10. r = 1 2 - cos u Find the polar equation of a parabola with focus at the pole, satisfying the given conditions. See Example 2. 11. The vertical directrix is 3 units to the right of the pole. 12. The vertical directrix is 4 units to the left of the pole. 13. The horizontal directrix is 5 units below the pole. 14. The horizontal directrix is 6 units above the pole. Find a polar equation for the conic with focus at the pole, satisfying the given conditions. Also identify the type of conic represented. See Example 2. 15. e = 4 5 , and the vertical directrix is 5 units to the right of the pole. 16. e = 2 3 , and the vertical directrix is 6 units to the left of the pole. 17. e = 5 4 , and the horizontal directrix is 8 units below the pole. 18. e = 3 2 , and the horizontal directrix is 4 units above the pole. Identify the type of conic represented by each equation. Then convert the equation to rectangular form. See Example 3. 19. r = 6 3 - cos u 20. r = 8 4 - cos u 21. r = -2 1 + 2 cos u 22. r = -3 1 + 3 cos u 23. r = -6 4 + 2 sin u 24. r = -12 6 + 3 sin u 25. r = 10 2 - 2 sin u 26. r = 12 4 - 4 sin u
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