Name: _____________________________
Class: _____________ Date: __________
Conics Multiple Choice Pre-Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1 Graph the equation x 2 + y 2 = 36. Then describe the graph and its lines of symmetry.
A
C
The graph is a circle of radius 36. Its
center is at the origin. Every line through
the center is a line of symmetry.
The graph is a circle of radius 6. Its
center is at the origin. Every line through
the center is a line of symmetry.
B
D
The graph is a circle of radius 6. Its
center is at the origin. The y-axis and the
x-axis are lines of symmetry.
The graph is a circle of radius 36. Its
center is at the origin. The y-axis and the
x-axis are lines of symmetry.
____
2 Graph the equation 16x 2 + 4y 2 = 49. 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 a circle. 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 Pre-Test
The graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
Page 2
____
3 Graph the equation x 2 − y 2 = 16. 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.
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
D
The graph is a circle with radius 4. Its
center is at the origin. Every line through
the center is a line of symmetry.
Algebra II Conics Pre-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 −3x 2 + 12y 2 = 84.
A
C
B
D
5 Write an equation of a parabola with a vertex at the origin and a focus at (-2, 0).
1
8
1
y = − x2
4
A x = − y2
C
B
D
1 2
x
8
1
x = y2
8
y=
6 Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.
A x = 5y 2
B
x = −
1 2
y
20
Algebra II Conics Pre-Test
1 2
x
20
C
y = −
D
y = −20x 2
Page 4
____
____
7 Identify the vertex, focus, and directrix of the graph of y =
1
(x − 2) 2 + 5.
8
A vertex (2, 5), focus (2, 7), directrix at y = 3
C vertex (2, -5), focus (0, -9), directrix at y = -1
B
D vertex (2, 5), focus (2, 3), directrix at y = 7
vertex (2, -5), focus (0, -1), directrix at y = -9
8 Graph x =
1 2
y .
5
A
C
B
D
Algebra II Conics Pre-Test
Page 5
____
9 Identify the conic section.
A Parabola
B Hyperbola
____
C Circle
D Ellipse
10 When a plane intersects a cone at an angle that is parallel to the edge of the cone, what shape is formed?
A Parabola
B Hyperbola
Algebra II Conics Pre-Test
C Circle
D Ellipse
Page 6
____
11 Write an equation of an ellipse with center (3, -3), vertical major axis of length 12, and minor axis of length
6. Graph the ellipse.
____
A
2
(y − 3) 2
(x + 3)
−
=1
6
12
C
2
(y − 3) 2
(x + 3)
−
=1
36
9
B
2
(y + 3) 2
(x − 3)
+
=1
12
6
D
2
(y + 3) 2
(x − 3)
+
=1
9
36
12 Write an equation of a circle with center (-5, 8) and radius 2.
2
2
A (x + 5) 2 + ÁËÊ y − 8 ˆ˜¯ = 2
C (x − 5) 2 + ÁËÊ y + 8 ˆ˜¯ = 4
2
2
B (x − 5) 2 + ÁËÊ y + 8 ˆ˜¯ = 2
D (x + 5) 2 + ÁËÊ y − 8 ˆ˜¯ = 4
Algebra II Conics Pre-Test
Page 7
____
13 Write an equation in standard form for the circle.
A
B
____
2
2
(x − 1) + ÁËÊ y − 3 ˆ˜¯ = 4
2
2
(x + 1) + ÁËÊ y + 3 ˆ˜¯ = 4
C
D
2
2
(x + 1) + ÁËÊ y − 3 ˆ˜¯ = 4
2
2
(x − 1) + ÁËÊ y + 3 ˆ˜¯ = 4
2
14 Find the center and radius of the circle with equation (x − 5) 2 + ÊÁË y + 6 ˆ˜¯ = 50.
A (5, -6); 5 2
C (5, -6); 25
B (-5, 6); 25
D (-5, 6); 5
Algebra II Conics Pre-Test
Page 8
____
2
15 Graph (x + 4) + ÊÁË y − 7 ˆ˜¯ = 49.
A
2
B
Algebra II Conics Pre-Test
C
D
Page 9
____
16 Identify the center of the hyperbola with the equation
2
(y + 4) 2
(x − 2)
−
= 1. Graph the hyperbola.
9
64
A center: (2, -4)
C center: (-2, 4)
B
D center: (-2, 4)
center: (2, -4)
Algebra II Conics Pre-Test
Page 10
____
17 Graph the ellipse with the equation
(x − 3) 2
(y + 2) 2
+
= 1.
49
64
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.
____
18 4x 2 + 7y 2 + 32x − 56y + 148 = 0
A ellipse with center (4, -4)
B
foci at (4 ± 3, -4)
hyperbola with center (-4, 4)
foci at (4, -4 ± 3)
Algebra II Conics Pre-Test
C ellipse with center (-4, 4)
D
foci at (−4 ± 3, 4)
hyperbola with center (4, -4)
foci at (−4, 4 ± 3)
Page 11
____
____
19 y 2 − 4x + 6y + 29 = 0
A parabola; vertex (-5, 3)
C parabola; vertex (5, 4)
B
D parabola; vertex (4, 3)
parabola; vertex (5, -3)
20 11x 2 − 3y 2 − 88x + 18y + 116 = 0
A ellipse with center (4, 3)
B
____
foci at (4, -3 ± 14)
hyperbola with center (4, 3)
foci at (4 ± 14, 3)
C ellipse with center (4, -3)
D
foci at (−4, 3 ± 14)
hyperbola with center (4, -3)
foci at (−3 ± 14, -4)
21 x 2 + y 2 + 8x − 4y = −11
A cirlce; center (-4, 2); radius = 9
B cirlce; center (4,- 2); radius = 9
Algebra II Conics Pre-Test
C cirlce; center (-4, 2); radius = 3
D cirlce; center (4,- 2); radius = 3
Page 12
____
22 In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 50
centimeters tall and 90 centimeters wide. Where should the filament be placed in the searchlight to acheive
the brightest beam?
____
A 10.125 cm from the vertex
C 20.25 cm from the vertex
B
D at the vertex
5 cm from the vertex
23 Write an equation of a circle with center (3, -7) that goes through the point (1, 1).
A (x + 3) 2 + (y − 7) 2 =52
C (x − 3) 2 + (y + 7) 2 =32
(x − 3) 2 + (y + 7) 2 =68
D (x + 3) 2 + (y − 7) 2 =40
B
Algebra II Conics Pre-Test
Page 13
____
____
24 Write an equation of a hyperbola with center (-4, 6) and vertices at (-8, 6) and (0, 6). Graph the hyperbola.
A
2
(y − 6) 2
(x + 4)
−
=1
16
9
C
(y − 6) 2 (x + 4) 2
−
=1
16
9
B
(y + 6) 2 (x − 4) 2
−
=1
16
9
D
2
(y + 6) 2
(x − 4)
−
=1
16
9
25 Write an equation for the translation of x 2 + y 2 = 25, 2 units right and 4 units down.
A
B
2
2
(x + 2) + ÁËÊ y + 4 ˜¯ˆ = 25
2
2
(x − 2) + ÁËÊ y + 4 ˜¯ˆ = 25
Algebra II Conics Pre-Test
C
D
2
2
(x + 2) + ÁËÊ y − 4 ˜¯ˆ = 25
2
2
(x − 2) + ÁËÊ y − 4 ˜¯ˆ = 25
Page 14
____
26 Find the center of the ellipse with the equation
2
(y − 2) 2
(x − 3)
+
= 1. Graph the ellipse.
49
64
A Center: (-3, -2)
C Center: (3, 2)
B
D Center: (3, 2)
Center: (-3, -2)
Algebra II Conics Pre-Test
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