Precalculus:  Graphing, Data, and Analysis

Chapter 11: Analytic Geometry


1. Find the equation of a parabola whose vertex is at the origin and directrix is the line 11m3q1.gif [Hint]

2. Which of the following is the graph of 11m3q2.gif [Hint]

3. Find the vertex, focus, and directrix of 11m3q3.gif. [Hint]

4. Find the equation of a parabola whose focus is (–2, 1) and directrix is the line 11m3q4.gif [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 11m3q6.gif [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 11m3q8.gif [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 11m3q10.gif [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 11m3q12.gif [Hint]

13. Find the equation of the hyperbola whose vertices are (0, –2) and (6, –2) that has an asymptote 11m3q13.gif [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: 11m3q16.gif [Hint]

17. Graph 11m3q17.gif. [Hint]

18. Graph 11m3q18.gif [Hint]

19. Graph the curve 11m3q19.gif11m3q19_2.gif11m3q19_3.gif [Hint]

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