Algebra 2
NAME________________
Chapter 9 Test (A)
Match each equation to the description of its graph
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1.
x2  y 2  4
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2.
x 2  16y
A. parabola with focus (4,0)
B. ellipse with foci @ (0,  5)
C. parabola with vertex (1, 2)
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3.
( x  1)2  4( y  2)
D. hyperbola with asymptotes
y
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4.
9x 2  4y 2  36
2
x
3
and
y 
2
x
3
E. circle with center (0,0) and radius 2
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5.
4x 2  y 2  8x  4y  4  0
6.
y 2  16x
7.
x  y  2x  4y  1  0
F. ellipse with foci @ (5,9)
and
(5,1)
G. parabola with directrix y  4
H. hyperbola with one of its vertices @ ( 2,  2)
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8.
9.
2
2
I.
parabola with x-axis for its line of symmetry and
focus @ (2,0)
J.
circle with center (1, 2) and radius of 2
9y 2  4x 2  36
y 2  8x
10. 4( x  5)2  3( y  5)2  192
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Choose the BEST answer.
11. Identify: 9x 2  25y 2  225  0
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A. Parabola
B. Circle
C. Ellipse
D. Hyperbola
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12. The center and radius of the circle x 2  y 2  4x  2y  4  0 are:
A. (2,  1) ; 2
(2,1) ; 2
C. (2,  1) ; 1
D. ( 2,1) ; 1
B.
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13. What is the equation of the parabola with vertex at (2, 3) and focus at (2, 7) ?
A.
( x  2)2  7( y  3)
B.
( x  2)2  16( y  3)
C. ( x  2)2  8( y  3)
D. ( x  2)2  ( y  3)
E.
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14. What is the length of the major axis of the ellipse
A.
B.
C.
D.
E.
________
( x  2)2  4( y  3)
x2 y 2

 1?
49 36
7
12
49
75
14
15. Find the equation of the parabola with its focus @ ( 4, 7) and directrix @ y  1 .
1
( x  4)2
24
1
B. y  4 
( x  4)2
12
1
C. y  4  
( x  4)2
12
1
D. y  3 
( x  4)2
24
A.
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y 7 
16. What is the equation of the directrix of the parabola y 2  x with its focus @ ( 
1
4
B. x  0
A.
x
1
4
D. y  1
C.
y 
1
, 0) ?
4
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17. The parabola 3  x 2  6x  y opens:
A. Up
B. Down
C. Left
D. Right
18. Identify: 7x 2  4y 2  24
A. Parabola
B. Circle
C. Ellipse
D. Hyperbola
19. What are the equations of the asymptotes of the hyperbola
y 2 x2

 1?
49 25
5
x
7
7
B. y   x
5
49
C. y  
x
25
25
D. y  
x
49
A.
_________
y 
20. What is the standard equation of an ellipse with center at the origin and whose x-intercepts
are 5 and whose y-intercepts are 3 ?
x2 y 2

5
3
2
x
y2
B.

16 9
x2 y 2
C.

25 9
x2 y 2
D.

25 16
A.
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_________
1
1
1
1
21. Identify: 4( x  3)2  4( y  2)2  16
A. Parabola
B. Circle
C. Ellipse
D. Hyperbola
22. Find the equation of a circle with center @ C ( 4, 3) and passes through the point P (2, 4) .
A.
( x  4)2  ( y  3)2  37
B.
( x  4)2  ( y  3)2  5
C. ( x  2)2  ( y  4)2  37
D. ( x  4)2  ( y  3)2  5
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23. Find the standard equation of a hyperbola with asymptotes y  
3
x and foci (0,  73) ?
8
y 2 x2

1
9 64
x2 y 2
B.

1
8
3
x2 y 2
C.

1
64 9
y 2 x2
D.

1
8
3
A.
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24. What is the equation of the circle?
2
-5
5
-2
-4
-6
A.
x2  y 2  5
B.
( x  2)2  ( y  2)2  25
C.
x 2  y 2  25
D. ( x  2)2  ( y  2)2  25
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25. What is the equation of the hyperbola below with asymptotes of y  
6
4
2
-5
5
-2
-4
-6
2
x
3
y2
B.
4
x2
C.
9
y2
D.
16
A.
2
y
4
x2

3
y2

16
x2

9

1
1
1
1
4
x?
3
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26. Choose the correct graph for the
equation ( x  3)2  4( y  2)2  16 .
A.
C.
4
4
2
2
5
10
-5
5
-2
-2
-4
-4
-6
-6
D.
B.
6
6
4
4
2
2
-5
-5
5
5
-2
-2
-4
-4
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27. Find the length of the line segment joining (3,  1) and ( 1, 5) .
28. If M ( 1, 5) is the midpoint of the segment PQ and P has coordinates of (3,  1) ,
then Q has coordinates of:
29. Find the coordinates of the vertex of the parabola having the equation
y  2  3x 2  6x .
30. What is the standard equation of a circle with center @ (2,  7) and radius of 4?
x2
y2

 1 has its center at the origin. If the center were moved to
________________ 31. The equation
9
4
C( 1, 2) , what would be the standard equation?
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32. Find the equation of an ellipse having foci at (0,  4) and length of minor axis of 10.
33. What are the coordinates of the foci of the hyperbola 16y 2  9x 2  144 ?