HPC: 10.2-10.4 In-Class Review
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Find the vertex, focus, and directrix of the parabola, and sketch its graph.
3
1. (𝑦 + 7)2 = 4 (𝑥 − 2)
1
2. 𝑦 = 4 (𝑥 2 − 2𝑥 + 5)
Find the standard form of the equation of the parabola with the given characteristics.
4. Vertex: (−2, 1); Directrix: 𝑥 = 1
3.
Find the center, vertices, foci, and eccentricity of the ellipse, and sketch its graph.
5.
(𝑥+5)2
9
4
2
+ (𝑦 − 1) = 1
6. 36𝑥 2 + 9𝑦 2 + 48𝑥 − 36𝑦 + 43 = 0
(𝑥+5)2
9
4
(𝑦 − 1)2
+
Find the standard form of the equation of the ellipse with the given characteristics.
8. Center: (−2, 2); 𝑎 = 5𝑐;
Foci: (−2,0), (−2, 4)
7.
9. Foci: (−6, 5), (2, 5);
4
Eccentricity: 5
Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch its graph.
10.
(𝑦−1)2
1
4
−
(𝑥+3)2
1
16
=1
11. 9𝑥 2 − 𝑦 2 + 54𝑥 + 10𝑦 + 55 = 0
(𝑥+3)2
1
16
Find the standard form of the equation of the hyperbola with the given characteristics.
12. Vertices: (4, 1), (4, 9);
Foci: (4, 0), (4, 10)
13. Vertices: (0, −3), (4, −3);
passes through the point
(−4, 5)
14. Foci: (−1, −1), (9, − 1);
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Asymptotes: 𝑦 = 4 𝑥 − 4,
3
𝑦 = −4𝑥 + 2
15. An engineer is designing headlight units for automobiles. The unit has a parabolic surface with a
diameter of 12 inches and a depth of 3 inches. What is the equation of the parabola in this system?
(Assume the vertex is at the origin of a coordinate system and that the parabolic surface opens up.)
Where should the light source be placed? Describe this placement relative to the vertex.