NAME ______
MAT 150 – Homework 17
Sections 5.2 and 5.3
Directions: Show all work and write your final answer in the space provided.
1. Find the equation of the parabola with vertex at (0, 0) and focus at (–4, 0). 1. ______
2. Find the equation of the ellipse with center at (0, 0), focus at (0, 1), and vertex 2. ______
at (0, –2).
3. Find the vertex, focus, and directrix of the parabola (x + 4)2 = 16(y + 2). Vertex: ______
Focus: ______
Drtx: ______
4. Find the center, vertices, and foci of the ellipse 9x2 + 4y2 = 36. Center: ______
Vertex: ______
Foci: ______
5. Find the equation of the parabola with vertex at (0, 0), symmetric to the x-axis, 5. ______
containing the point (2, 3).
6. Find the center, vertices, and foci of the ellipse (x +5)2 + 4(y – 4)2 = 16. Center: ______
Vertex: ______
Foci: ______
7. Find the equation of the parabola with vertex at (4, –2) and focus at (6, –2). 7. ______
8. Find the equation of the ellipse with foci at (0, ±2) and the length of the major axis 8. ______
is 8.
9. Find the center, vertices, and foci of the ellipse 9(x – 3)2 + (y + 2)2 = 18. Center: ______
Vertex: ______
Foci: ______
10. Find the vertex, focus, and directrix of the parabola (y + 3)2 = 8(x – 2). Vertex: ______
Focus: ______
Drtx: ______
11. Find the equation of the ellipse with vertices at (2, 5) and (2, –1) and c = 2. 11. ______
12. Find the equation of the parabola with focus at (–4, 4) and directrix at y = –2. 12. ______
13. Find the center, vertices, and foci of the ellipse x2 + 3y2 – 12y + 9 = 0. Center: ______
Vertex: ______
Foci: ______
14. Find the vertex, focus, and directrix of the parabola y2 + 12y = –x + 1. Vertex: ______
Focus: ______
Drtx: ______
15. Find the center, vertices, and foci of the ellipse 4(x – 1)2 + 25(y + 3)2 = 100. Center: ______
Vertex: ______
Foci: ______
16. Find the vertex, focus, and directrix of the parabola x2 + 6x – 4y + 1 = 0. Vertex: ______
Focus: ______
Drtx: ______
17. Find the equation of the ellipse with center at (–3, 1), vertex at (–3, 3), and focus at 17. ______
(–3, 0).
18. Find the center, vertices, and foci of the ellipse 9x2 + 4y2 – 18x + 16y – 11 = 0. Center: ______
Vertex: ______
Foci: ______
19. A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the 19. ______
location of the receiver, which is placed at the focus, if the dish is 6 feet across at
its opening at 2 feet deep.
20. Find the equation of the ellipse with center at (1, 2), vertex at (1, 4), and containing 20. ______
the point (2, 2).