Name: Class: Date: - TBAISD Moodlemoodle.tbaisd.org/pluginfile.php/68305/mod_resource/content/0/... · Algebra II Conics Pre-Test Page 3 ____ 3 Graph the equation x2 − y2 = 16

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 x2

+ y2

= 36. Then describe the graph and its lines of symmetry.

A

The graph is a circle of radius 6. Its

center is at the origin. Every line through

the center is a line of symmetry.

C




B


center is at the origin. The y-axis and the

x-axis are lines of symmetry.

D


center is at the origin. The y-axis and the

x-axis are lines of symmetry.

Algebra II Conics Pre-Test Page 2

____ 2 Graph the equation 16x2

+ 4y2


A

The graph is an ellipse. The center is at

the origin. It has two lines of symmetry,

the x-axis and the y-axis.

C

The graph is a circle. The center is at the

origin. Every line through the origin is a

line of symmetry.

B

The graph is an ellipse. The center is at



D

The graph is a circle. The center is at the

origin. Every line through the origin is a

line of symmetry.


____ 3 Graph the equation x2

− y2


A

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.

C


the origin. It has four lines of symmetry,

the x-axis, the y-axis, y = x, and y = –x.

B

The graph is a circle with radius 4. Its



D





____ 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).

A x = −1

8y

2 C y =1

8x

2

B y = −1

4x

2 D x =1

8y

2

____ 6 Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.

A x = 5y 2 C y = −1

20x 2

B x = −1

20y 2 D y = −20x2


____ 7 Identify the vertex, focus, and directrix of the graph of y =1

8(x − 2)2 + 5.

A vertex (2, 5), focus (2, 7), directrix at y = 3 C vertex (2, -5), focus (0, -9), directrix at y = -1

B vertex (2, -5), focus (0, -1), directrix at y = -9 D vertex (2, 5), focus (2, 3), directrix at y = 7

____ 8 Graph x =1

5y 2 .

A C

B D


____ 9 Identify the conic section.

A Parabola C Circle

B Hyperbola 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 C Circle

B Hyperbola D Ellipse


____ 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.

Ax + 3( )

2

6−

(y − 3)2

12= 1 C

x + 3( )2

36−

(y − 3)2

9= 1

Bx − 3( )

2

12+

(y + 3)2

6= 1 D

x − 3( )2

9+

(y + 3)2

36= 1

____ 12 Write an equation of a circle with center (-5, 8) and radius 2.

A x + 5( )2

+ y − 8ÊËÁÁ ˆ

¯˜̃

2= 2 C x − 5( )

2+ y + 8ÊËÁÁ ˆ

¯˜̃

2= 4

B x − 5( )2

+ y + 8ÊËÁÁ ˆ

¯˜̃

2= 2 D x + 5( )

2+ y − 8ÊËÁÁ ˆ

¯˜̃

2= 4


____ 13 Write an equation in standard form for the circle.

A x − 1( )2


¯˜̃

2= 4 C x + 1( )


¯˜̃

2= 4

B x + 1( )2

+ y + 3ÊËÁÁ ˆ

¯˜̃

2= 4 D x − 1( )

2+ y + 3ÊËÁÁ ˆ

¯˜̃

2= 4

____ 14 Find the center and radius of the circle with equation x − 5( )2

+ y + 6ÊËÁÁ ˆ

¯˜̃

2= 50.

A (5, -6); 5 2 C (5, -6); 25

B (-5, 6); 25 D (-5, 6); 5


____ 15 Graph x + 4( )2


¯˜̃

2= 49.

A C

B D


____ 16 Identify the center of the hyperbola with the equation x − 2( )

2

9−

(y + 4)2

64= 1. Graph the hyperbola.

A center: (2, -4) C center: (-2, 4)

B center: (2, -4) D center: (-2, 4)


____ 17 Graph the ellipse with the equation (x − 3)2

49+

(y + 2)2

64= 1.

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)

foci at (4 ± 3, -4)

C ellipse with center (-4, 4)

foci at (−4 ± 3, 4)

B hyperbola with center (-4, 4)

foci at (4, -4 ± 3)

D hyperbola with center (4, -4)

foci at (−4, 4 ± 3)


____ 19 y 2 − 4x + 6y + 29 = 0

A parabola; vertex (-5, 3) C parabola; vertex (5, 4)

B parabola; vertex (5, -3) D parabola; vertex (4, 3)

____ 20 11x 2 − 3y 2 − 88x + 18y + 116 = 0

A ellipse with center (4, 3)

foci at (4, -3 ± 14)

C ellipse with center (4, -3)

foci at (−4, 3 ± 14)

B hyperbola with center (4, 3)

foci at (4 ± 14, 3)

D hyperbola with center (4, -3)

foci at (−3 ± 14, -4)

____ 21 x2

+ y2

+ 8x − 4y = −11

A cirlce; center (-4, 2); radius = 9 C cirlce; center (-4, 2); radius = 3

B cirlce; center (4,- 2); radius = 9 D cirlce; center (4,- 2); radius = 3


____ 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 5 cm from the vertex D at 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

B (x − 3)2

+ (y + 7)2

=68 D (x + 3)2

+ (y − 7)2

=40


____ 24 Write an equation of a hyperbola with center (-4, 6) and vertices at (-8, 6) and (0, 6). Graph the hyperbola.

Ax + 4( )

2

16−

(y − 6)2

9= 1 C

(y − 6)2

16−

(x + 4)2

9= 1

B(y + 6)

2

16−

(x − 4)2

9= 1 D

x − 4( )2

16−

(y + 6)2

9= 1

____ 25 Write an equation for the translation of x2

+ y2

= 25, 2 units right and 4 units down.

A x + 2( )2

+ y + 4ÊËÁÁ ˆ

¯˜̃

2= 25 C x + 2( )


¯˜̃

2= 25

B x − 2( )2

+ y + 4ÊËÁÁ ˆ

¯˜̃

2= 25 D x − 2( )


¯˜̃

2= 25


____ 26 Find the center of the ellipse with the equation x − 3( )

2

49+

(y − 2)2

64= 1. Graph the ellipse.

A Center: (-3, -2) C Center: (3, 2)

B Center: (-3, -2) D Center: (3, 2)

Documents

Name: Class: Date: - TBAISD Moodlemoodle.tbaisd.org/pluginfile.php/68305/mod_resource/content/0/... · Algebra II Conics Pre-Test Page 3 ____ 3 Graph the equation x2 − y2 = 16