# Chapter 11: Analytic Geometry

## Test

1. Find the equation of a parabola whose vertex is at the origin and directrix is the line [Hint]

2. Which of the following is the graph of [Hint]

3. Find the vertex, focus, and directrix of . [Hint]

4. Find the equation of a parabola whose focus is (–2, 1) and directrix is the line [Hint]

5. Find the equation of an ellipse whose foci and (0, –4) and (0, 4) and vertex is (0, 7). [Hint]

6. Graph the equation [Hint]

7. Find an equation for the ellipse with center (1, –3), one focus at (1, 1), and one vertex at (1, 2). [Hint]

8. Graph [Hint]

9. Find an equation of the hyperbola with center at the origin, one focus at (0, –5) and one vertex at (0, –2). [Hint]

10. Find the center, vertices, foci and asymptotes of [Hint]

11. Find an equation of the hyperbola with center (–1, 3), focus at (–1, 7), and vertex at (–1, 5). [Hint]

12. Find the center, vertices, foci, and asymptotes of the hyperbola [Hint]

13. Find the equation of the hyperbola whose vertices are (0, –2) and (6, –2) that has an asymptote [Hint]

14. A microphone is located 6 inches from the base of a paraboloid of revolution along the axis of symmetry. If the opening is 36 inches across, how deep should the paraboloid be in order to maximize the amount of sound picked up by the microphone? [Hint]

15. A hall 120 feet in length is to be designed as a whispering gallery. If the foci are located 40 feet from the center, how high will the ceiling be at the center? [Hint]

16. Identify the conic: [Hint]

17. Graph . [Hint]

18. Graph [Hint]

19. Graph the curve [Hint]

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