Chapter 10 Test Review
10-2 Parabolas
1. Write the equation of a parabola with vertex at the origin and a focus at the following. Then graph the parabola.
a. (0, -4)
b. (-1, 0)
c. (0, -5)
2. Identify the vertex, focus, and directrix of the parabola. Sketch the graph and identify the domain and range.
a.y=x2+4x+3
b. y=x2+8x+13
c. y=x2-8x+10
3. Write the equation of a parabola with the given vertex and focus
a. vertex: (4, 1) focus: (6, 1)
b. vertex: (7, 2) focus: (7, -2)
c. vertex: (4, 7) focus: (4, 4)
10-3 Circles
4. Write the equation of a circle with the given center and radius. Sketch the graph.
a. center: (2, 0) radius: 1
b. center: (2, 3) diameter: 1
c. center: (1, -5) radius: 2.5
5. Graph the circle and identify the domain and range.
a. x2+y2=144
b. (x-6)2+(y-9)2=4
c. x2+(y+3)2=9
10-4 Ellipses
6. Write the equation of the ellipse given the following information.
a. Center: origin, vertex: (0, 6), co-vertex: (1, 0)
b. horizontal ellipse with major axis: 30, minor axis: 18
c. foci: (0, ±8), co-vertices: (±8, 0)
d. foci: (0, ±4), co-vertices: (±2, 0)
7. Graph the ellipse. Identify the domain and range.
a. x225+y216=1
b. 3x2+y2=9
c. 36x2+8y2=288
10-5 Hyperbolas
8. Write an equation of a hyperbola with the given value. Assume the transverse axis is horizontal.
a. a=3, b=4
b. foci (±13, 0), vertices (±12, 0)
c. foci: (±5, 0), vertices (±2, 0)
9. Find the vertex, foci, and asymptotes of each hyperbola. Then sketch the graph and indentify the domain and range.
a. 14y2-28x2=448
b. 36x2-8y2=288
c. y225-x2100=1
10-6 Translating Conic Sections
10. Identify the center, vertices, and foci of each hyperbola.
a. (x+11)216-y29=1
b. (y-9)249-(x-3)24=1
c. (x-5)225-(y-2)275=1
11. Write the standard form equation of an ellipse with the given characteristics. Sketch the ellipse indentify the domain and range.
a. Vertex: (7, 3) and (-3, 3), focus: (5, 3)
b. vertex: (11, -8) and (-19, -8), focus: (5, -8)
c. vertex: (3, 6) and (3, -2), focus (3, 5)