Algebra 2
Chapter 13 Test Review
Name________________
Date_________________
Find the midpoint and distance between each pair of points whose coordinates are given.
Express answers in simplest form.
1. (-2, -4) and (3, 4)
2. (2, -5) and (-3, -1)
3. (5, 2) and (-1, 4)
Midpoint ___________
Midpoint ___________
Midpoint ___________
Distance ___________
Distance ___________
Distance ___________
Graph the circle. Identify the center and radius.
2
2
4. y 2   x 2  9
5.  x  2    y  3  30
4.______________
Center
________________
Radius
5.______________
Center
________________
Radius
Write the equation of the circle that satisfies the given information.
6. Center (0, 0) r = 9
7. Center (3, -5) r  2 5
8.
Center (0, 0) and the point
on the circle (-3, 5)
9.
Center (0, 0) and the point
on the circle (4, -6)
Find the coordinates of the foci of the ellipse centered at the origin with the given information.
10. Vertices: (0, -4) (0, 4);
11. Vertices: (-3, 0) (3, 0);
Co-vertices: (-2, 0) (2, 0)
Co-vertices: (0, -1) (0, 1)
Graph the ellipse. Identify the vertices, co-vertices, and foci of the ellipse.
x2 y2
x2 y2
12.
13.

1

1
9 25
36 8
12._____________
Vertices
________________
Co-Vertices
________________
Foci
13._____________
Vertices
________________
Co-Vertices
________________
Foci
y2
1
14. x 
7
2
15. 2 x 2  25 y 2  50
14._____________
Vertices
________________
Co-Vertices
________________
Foci
15._____________
Vertices
________________
Co-Vertices
________________
Foci
Write an equation of an ellipse that satisfies the given information.
16. Center (0, 0); Vertex (0, -6);
17. Center (0, 0); Vertex (7, 0);
Co-Vertex (4, 0)
Co-Vertex (0, 3)
18. Center (0, 0); Vertex (0, -8);
Focus (0, 1)
19. Center (0, 0); Vertex (-9, 0);
Focus (3, 0)
Graph the parabola. Label the focus, directrix, and axis of symmetry.
9
1
20. y 2  x
21. x 2  y
2
3
Focus:_______________
Focus:_______________
Directrix:_____________
Directrix:_____________
Axis of Symmetry:______
Axis of Symmetry:______
x
x
y
y
Write the equation of the parabola with its vertex at the origin that fits the given conditions.
 3
22. Focus (-3, 0)
23. Focus  0, 
 8
24. Directrix y = - 5
25. Directrix x = 6
Identify the vertices and foci of the hyperbola.
x2 y2
26.

1
16 25
27.
y2 x2

1
4 49
Graph the hyperbola. Identify the asymptotes, vertices, and foci.
x2 y2
y2 x2
28.
29.

1

1
49 16
9 36
28._____________
Asymptotes
________________
Vertices
________________
Foci
29._____________
Asymptotes
________________
Vertices
________________
Foci
30. 36 x 2  9 y 2  36
30._____________
Asymptotes
________________
Co-Vertices
________________
Foci
Write an equation of a hyperbola that satisfies the given conditions.
31. Foci (-7, 0) (7, 0)
32. Foci (0, -5) (0, 5)
Vertices (-4, 0) (4, 0)
Vertices (0, -3) (0, 3)
33. Foci (0, -2) (0, 2)
Vertices (0, -1) (0, 1)
34. Foci (-3, 0) (3, 0)
Vertices (-2, 0) (2, 0)
Identify the conic section from its equation.
A) For circles, also identify the radius
B) For ellipses, also identify the vertices, co-vertices, and foci
C) For parabolas, also identify the axis of symmetry, focus, and directrix
D) For hyperbolas, also identify the vertices and foci
35.
y2
x
16
36.
x2 y2

1
16 64
y2
37. x 
1
14
38. x 2  7 y
39. 20 x 2  20 y 2  80
40. 4 y 2  6 x 2  12
2
Answer Key
1. MP = (1/2, 0) d =√89
4.
2. MP(-1/2, -3) d =√41
5.
3. MP = (2, 3) d =2√10
6. 𝑥 2 + 𝑦 2 = 81
7.
(𝑥 − 3)2 + (𝑦 + 5)2 = 20
8.
𝑥 2 + 𝑦 2 = 34
9. 𝑥 2 + 𝑦 2 = 52
10. (0,2√3) (0, -2√3) 11. (2√2, 0) (-2√2, 0)
C: (0, 0) r = 3
12.
V: (0, ±5)
CV: (±3, 0)
F: (0, ±4)
C: (2, -3) r = √30
13.
V: (±6, 0)
CV: (0, ±2√2)
F: (±2√7, 0)
14.
V: (0, ±√7)
CV: (±1, 0)
F: (0, ±√6)
15.
V: (±5, 0)
CV: (0, ±√2)
F: (±√23, 0)
16.
𝑥2
16
𝑦2
+ 36 = 1
𝑥2
49
17.
+
𝑦2
9
=1
18.
9
2
20. 𝑦 2 = 𝑥
9
Focus (8 , 0)
Focus
9
−8
3
2
23. 𝑥 2 = 𝑦
𝑥2
81
𝑦2
+ 72 = 1
1
𝑦2
29.
4
𝑥2
30. 36𝑥 2 − 9𝑦 2 = 36
− 36 = 1
Asymptotes: y = ± x
2
Vertices (0, -3) (0, 3)
Foci (0, 3√5) (0, -3√5)
𝑦2
9
32.
𝑥2
− 16 = 1
33.
𝑦2 −
Asymptotes: y = ±4x
Vertices (1, 0) (-1, 0)
Foci (√5, 0) (-√5, 0)
𝑥2
3
=1
34.
𝑥2
4
−
𝑦2
5
=1
36. Ellipse V: (0, ±8), CV: (±4, 0) 37. Hyperbola V: (±1 , 0)
F: (0, ±4√3)
F: (±√15, 0)
35. parabola F(4, 0) dir. x = -4
7
𝑦2
9
1
Asymptotes: y = ± x
7
Vertices (-7, 0) (7, 0)
Foci (-√65, 0) (√65, 0)
𝑦2
𝑦 2 = −24𝑥
25.
27. V: (0, ±2); F: (0, ±√53)
− 16 = 1
31. 16 − 33 = 1
𝑥 2 = 20𝑦
24.
26. V: (±4, 0); F: (±√41, 0)
𝑥2
1
3
1
(0, 12)
19.
Directrix 𝑦 = − 12
Axis of Symmetry
y-axis
22. 𝑦 2 = −12𝑥
𝑥2
49
𝑦2
+ 64 = 1
21. 𝑥 2 = 𝑦
Directrix 𝑥 =
Axis of symmetry
x-axis
28.
𝑥2
63
7
38. parabola F(0, 4) dir. 𝑦 = − 4
39. Circle r = 2
40. Hyperbola V: (0, ±√3)
F: (0, ±√5)