Name: _____________________________
Class: _____________ Date: __________
Conics Multiple Choice Post-Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1 Graph the equation x = 4(y − 2) 2 + 1. Then describe the graph and its lines of symmetry.
A
C
The graph is a parabola.Its vertex is at
the point (1, 2). The line y = 2 is the only
line of symmetry.
B
The graph is a parabola. Its vertex is at
the point (-1, 2). The line y = 2 is the
only line of symmetry.
D
The graph is a parabola. Its vertex is at
the point (1, 2). The lines y = 2 and x = 1
are lines of symmetry.
The graph is a parabola. Its vertex is at
the point (1, 2). The lines y = 2 and x = 1
are lines of symmetry.
____
2 Graph the equation 4x 2 + 9y 2 = 36. Then describe the graph and its lines of symmetry.
A
C
The graph is an ellipse. The center is at
the origin. It has two lines of symmetry,
the x-axis and the y-axis.
B
The graph is an ellipse. The center is at
the origin. Every line through the origin
is a line of symmetry.
D
The graph is an ellipse. The center is at
the origin. It has two lines of symmetry,
the x-axis and the y-axis.
Algebra II Conics Post-Test
The graph is an ellipse. The center is at
the origin. Every line through the origin
is a line of symmetry.
Page 2
____
3 Graph the equation 16x 2 − 4y 2 = 64. Then describe the graph and its lines of symmetry.
A
C
The graph is a hyperbola. Its center is at
the origin. It has four lines of symmetry,
the x-axis, the y-axis, y = x, and y = –x.
B
The graph is a hyperbola. Its center is at
the origin. It has four lines of symmetry,
the x-axis, the y-axis, y = x, and y = –x.
D
The graph is a hyperbola with. Its center
is at the origin. Every line through the
center is a line of symmetry.
Algebra II Conics Post-Test
The graph is a hyperbola. Its center is at
the origin. It has two lines of symmetry,
the x-axis and the y-axis.
Page 3
____
4 Graph 5x 2 + 10y 2 = 50.
A
C
B
D
Algebra II Conics Post-Test
Page 4
____
____
5 Find the center of the ellipse with the equation
2
(y − 5) 2
(x + 1)
+
= 1. Graph the ellipse.
16
25
A Center: (-1, 5)
C Center: (1, -5)
B
D Center: (1, -5)
Center: (-1, 5)
6 Write an equation of a parabola with a vertex at the origin and a focus at (4, 0).
1 2
y
16
1
y = − x2
16
A x=−
C
B
D
Algebra II Conics Post-Test
1 2
x
16
1 2
x=
y
16
y=
Page 5
____
7 Write an equation of a parabola with a vertex at the origin and a directrix at y = -6.
A x = −6y 2
B
____
x =
1 2
y
24
C
D
1 2
x
24
1 2
y =
x
24
y = −
8 Identify the vertex, focus, and directrix of the graph of y =
A vertex (3, 5), focus (3, 6)
directrix at y = 4
B
vertex (3, -5), focus (2, -5)
directrix at x = 4
Algebra II Conics Post-Test
1
(x − 3) 2 − 5.
4
C vertex (3, -5), focus (4, -5)
directrix at x = 2
D vertex (3, 5), focus (3, 4)
directrix at y = 6
Page 6
____
9 Graph x =
1
(y − 2) 2 .
3
A
C
B
D
Algebra II Conics Post-Test
Page 7
____
10 Identify the conic section.
A Parabola
B Hyperbola
Algebra II Conics Post-Test
C Circle
D Ellipse
Page 8
____
____
11 Identify the center of the hyperbola with the equation
A center: (-3, -1)
C center: (3, 1)
B
D center: (3, 1)
center: (-3, -1)
12 When a plane intersects a cone at an angle that is parallel to the axis of the cone, what shape is formed?
A Parabola
B Hyperbola
____
2
(y + 1) 2
(x + 3)
−
= 1. Graph the hyperbola.
25
81
C Circle
D Ellipse
13 Write an equation of a circle with center (-3, -4) and radius 2.5.
A
B
2
2
(x + 3) + ÊÁË y + 4 ˜¯ˆ = 6.25
2
2
(x + 3) + ÁËÊ y + 4 ˆ˜¯ = 2.5
Algebra II Conics Post-Test
C
D
2
2
(x − 3) + ÊÁË y − 4 ˜¯ˆ = 6.25
2
2
(x − 3) + ÁËÊ y − 4 ˆ˜¯ = 2.5
Page 9
____
14 Write an equation in standard form for the circle.
A
B
____
2
2
(x − 3) + ÊÁË y − 7 ˆ˜¯ = 25
2
2
(x + 3) + ÁËÊ y + 7 ˆ˜¯ = 5
C
D
2
2
(x + 3) + ÊÁË y + 7 ˆ˜¯ = 25
2
2
(x − 3) + ÁËÊ y − 7 ˆ˜¯ = 5
2
15 Find the center and radius of the circle with equation (x − 15) 2 + ÊÁË y + 62 ˆ˜¯ = 500.
A center:(15, -62); radius = 5 10
C center: (15, -62); radius = 250
B
D center: (-15, 62); radius = 500
center: (-15, 62); radius = 250
Algebra II Conics Post-Test
Page 10
____
16 Write an equation of an ellipse with center (-2, 4), vertical major axis of length 10, and minor axis of length
8. Graph the ellipse.
A
2
(y − 4) 2
(x + 2)
−
=1
8
10
C
2
(y − 4) 2
(x + 2)
−
=1
25
16
B
2
(y + 4) 2
(x − 2)
+
=1
10
8
D
2
(y − 4) 2
(x + 2)
+
=1
16
25
Algebra II Conics Post-Test
Page 11
____
2
17 Graph (x − 2) + ÊÁË y + 7 ˆ˜¯ = 16.
2
A
C
B
D
Algebra II Conics Post-Test
Page 12
____
18 Graph the ellipse with the equation
(x − 4) 2
(y + 7) 2
+
= 1.
25
9
A
C
B
D
In the next three questions, identify the conic section. If it is a parabola, give the vertex. If it is a
circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci.
____
19 9x 2 + 16y 2 + 18x − 64y − 71 = 0
A ellipse with center (-1, 2)
foci at (−1 ±
B
7, 2)
hyperbola with center (-1, 2)
foci at (4, 2)and(−6, 2)
Algebra II Conics Post-Test
C ellipse with center (-1, 2)
foci at (−1, 2 ±
7)
D hyperbola with center (-1, 2)
foci at (−1, 7)and(−1, −3)
Page 13
____
____
20 x 2 − 8x − y + 19 = 0
A parabola; vertex (4, -3)
C parabola; vertex (-3, 4)
B
D parabola; vertex (3, 4)
parabola; vertex (4, 3)
21 9x 2 − 4y 2 − 24y = 72
A ellipse with center (0, -3)
foci at (±
B
____
5, -3)
hyperbola with center (0, -3)
foci at (± 13, -3)
C ellipse with center (0, 3)
foci at (0, 3 ±
5)
D hyperbola with center (0, 3)
foci at (0, 3 ±
13)
22 x 2 + y 2 − 6x + 8y = −16
A cirlce; center (-3, 4); radius = 9
C cirlce; center (3, -4); radius = 3
B
D cirlce; center (-3, 4); radius = 3
cirlce; center (3, -4); radius = 9
Algebra II Conics Post-Test
Page 14
____
23 The dimensions of the elliptical orbit of Earth and Mars are given below. The sun is on the negative y-axis
at one focus and the other focus is on the positive y-axis. Write an equation for each orbit. Which orbit is
the most circular?
Planet
a
b
Earth
149.60 million km
149.58 million km
Mars
227.9 million km
226.9 million km
A
y2
x2
+
=1
Earth :
149.60 2 149.58 2
y2
x2
+
=1
Mars:
227.92 226.9 2
C
Earth’s orbit is more circular
B
y2
x2
+
=1
149.60 2 149.58 2
y2
x2
+
=1
Mars:
227.92 226.9 2
Earth :
Mars’s orbit is more circular
y2
x2
+
=1
149.58 2 149.60 2
y2
x2
+
=1
Mars:
226.92 227.9 2
D Earth :
Mars’s orbit is more circular
____
Earth’s orbit is more circular
24 Write an equation of a circle with center (-2, -4) that goes through the point (2, -1).
A (x + 2) 2 + (y + 4) 2 = 25
B
____
y2
x2
+
=1
Earth :
149.58 2 149.60 2
y2
x2
+
=1
Mars:
226.92 227.9 2
(x − 2) 2 + (y − 4) 2 = 40
C (x − 2) 2 + (y − 4) 2 = 5
D (x + 2) 2 + (y + 4) 2 = 40
25 Write an equation for the translation of x 2 + y 2 = 36, 5 units left and 8 units up.
A
B
2
2
(x + 5) + ÁËÊ y − 8 ˜¯ˆ = 36
2
2
(x − 5) + ÁËÊ y − 8 ˜¯ˆ = 36
Algebra II Conics Post-Test
C
D
2
2
(x + 5) + ÁËÊ y + 8 ˜¯ˆ = 36
2
2
(x − 5) + ÁËÊ y + 8 ˜¯ˆ = 36
Page 15
____
26 Write an equation of a hyperbola with center (3, 5) and vertices at (3, 7) and (3, 3). Graph the hyperbola.
A
B
ÊÁ y − 3 ˆ˜ 2
(x − 5) 2
Ë
¯
−
=1
4
9
2
(y − 5) 2
(x − 3)
−
=1
9
4
Algebra II Conics Post-Test
C
D
ÊÁ y + 3 ˆ˜ 2
(x + 5) 2
Ë
¯
−
=1
4
9
2
(y + 5) 2
(x + 3)
−
=1
9
4
Page 16