College Algebra
Unit 5 (1.5, 10.2-10.5) Test Review
Name _____________________________________________
For 1-8, write the standard form for the following conic sections with the given information.
1.) a circle with radius 1 and center (–1, –2)
2.) a circle with center at the point (–2, 4) and tangent to the
x- axis
3.) a parabola with vertex at  2, 3 and focus at  2, 4 
4.) a parabola with focus at  2,0  and directrix x = 2
5.) an ellipse with foci at (–3, 0) and (3, 0); vertex at (4, 0)
6.) an ellipse with foci at (–4, 2) and (–4, 8); vertex at (–4, 10)
7.) a hyperbola with center at (0, 0); focus at (0, 4);
vertex at (0, –2)
8.) a hyperbola with center at (–2, -3); focus at (–4, –3);
vertex at (–3, –3)
For 9 & 10, use the equation of the parabola  y  1  4  x  2  to find the following:
2
9.) the vertex
For 11 & 12, use the equation of the ellipse
11.) the center
10.) the focus
 x  4
25
2

 y  2
16
2
 1 to find the following:
12.) the major vertices and the minor vertices
College Algebra
Unit 5 (1.5, 10.2-10.5) Test Review
For 13-15, use the equation of the hyperbola
13.) the vertices
 x  3
2
36
 y  4

2
 1 to find the following:
9
14.) the foci
15.) the equations of the asymptotes
For 16 & 17, find the standard form of the circle.
16.) x  y  2 x  4 y  4  0
2
2
17.) x  y  4 x  4 y  1  0
2
2
For 18 & 19, find the standard form of the parabola.
19.) x  4 x  2 y
18.) x  4 y  4
2
2
For 20 & 21, find the standard form of the ellipse.
20.) 4 x  9 y  16 x  18 y  11  0
2
2
21.) 9 x  4 y  18x  8 y  23
2
2
For 22 & 23, find the standard form of the hyperbola.
22.) y  4 y  4 x  8 x  4  0
2
2
23.) x  y  2 x  2 y  1  0
2
2
College Algebra
Unit 5 (1.5, 10.2-10.5) Test Review
For 24- 27, identify the equation without rewriting in standard form.
24.) y  4 x  3 y  8  0
2
26.) x  8 y  x  2 y  0
2
2
25.) x  2 y  4 x  8 y  2  0
2
2
27.) x  y  4 x  2 y  5  0
2
2
For 28 & 29, identify the center and radius of the circle, then graph.
 x  2
28.)  x  1   y  3  9
29.)
Center:
Center:
2
2
Radius:
2
  y  5   16
2
Radius:
For 30 & 31, identify the vertex, focus, and the equation of the directrix of the parabola, then graph.
30.) y 2  16 x
Vertex:
Directrix:
31.)
Focus:
 x  1
Vertex:
Directrix:
2
 4  y  3
Focus:
College Algebra
Unit 5 (1.5, 10.2-10.5) Test Review
For 32 & 33, identify the center, the four vertices, and the two foci of the ellipse, then graph.
32.)
x2 y 2

1
25 16
Center:
33.)
Vertices:
Foci:
 x  4
2
9
 y  3

2
1
25
Center:
Vertices:
Foci:
For 34 & 35, identify the center, the two vertices, the two foci, and the equations of the asymptotes of the hyperbola, then
graph.
x2 y 2
 1
34.)
25 1
35. )
 y  1
Center:
Vertices:
Center:
Foci:
Asymptotes:
Foci:
9
2
 x  2

16
2
1
Vertices:
Asymptotes:
College Algebra
Unit 5 (1.5, 10.2-10.5) Test Review