Conic Sections Practice Test

ID: A
Conic Sections Practice Test
1. Give the coordinates of the circle's center and it radius.
(x − 2)
____
2
+ (y + 9)
2
=1
2. Find the equation of the circle graphed below.
A) x
B)
y
2
2
+y
=x
2
2
=4
C)
x
+ 16
D) x
2
2
+y
+y
2
2
1
= 16
=1
E)
x
2
+ y = 16
Name: ______________________
____
ID: A
3. Graph the following equation.
x
2
− 10x + y
2
= -9
A)
C)
B)
____
4. Find the vertex and focus of the parabola.
ÁÊË y − 2 ˜ˆ¯ 2 + 16 (x − 3) = 0
A) vertex: ÊÁË −3, −2 ˆ˜¯
focus: ÊÁË −3, 14 ˆ˜¯
B) vertex: ÁÊË −3, −2 ˜ˆ¯
focus: ÁÊË −3, −18 ˜ˆ¯
C) vertex: ÊÁË −3, −2 ˆ˜¯
focus: ÊÁË −7, −2 ˆ˜¯
D) vertex: ÊÁË 3, 2 ˆ˜¯
focus: ÊÁË −1, 2 ˆ˜¯
2
Name: ______________________
____
ID: A
5. Find the standard form of the equation of the parabola with the given characteristic and vertex at
the origin.
focus: (0, 7)
A) x2 = 28y
B) x2 = 7y
____
C) x2 = –7y
D) y2 = 28x
E)
y2 = 7x
6. Find the standard form of the equation of the parabola with the given characteristic and vertex at
the origin.
directrix: x = 1
A) x2 = –4y
B) x2 = 4y
____
C) x2 = y
D) y2 = x
E)
y2 = –4x
7. Find the vertex and focus of the parabola.
= − 9x
8
ÊÁ
ˆ˜
A) vertex: ÁÁÁÁ 0, − 5 ˜˜˜˜
ÁË
4 ˜¯
y
2
B)
vertex: (0, 0)
C)
vertex: (0, 0)
D) vertex: (0, 0)
____
ÊÁ
ˆ˜
focus: ÁÁÁÁ − 9 , − 9 ˜˜˜˜
ÁË 8
8 ˜¯
ÊÁ
ˆ˜
focus: ÁÁÁÁ 0, − 9 ˜˜˜˜
ÁË
8 ˜¯
ÊÁ
ˆ˜
focus: ÁÁÁÁ − 9 , 0 ˜˜˜˜
ÁË 8
˜¯
ÁÊ
˜ˆ
focus: ÁÁÁÁ − 9 , 0 ˜˜˜˜
ÁË 32
˜¯
8. Find the equation of the parabola with vertex at (5, 4) and focus at (-3, 4).
A) ( y − 4 )
B)
(y − 4)
C)
(y + 4)
2
2
2
= − 32( x − 5 )
D) ( y + 4 )
= 32( x − 5 )
E) ( y − 4 )
2
2
= − 32( x − 5 )
= 8( x − 5 )
= 32( x + 5 )
9. Find the equation of the parabola with vertex at (0, 0) and focus at (0, 5). Express the equation in
standard form.
3
Name: ______________________
____
ID: A
10. Find the center and vertices of the ellipse.
2
2
x + y
49
4
A)
B)
C)
D)
____
= 1
center: (7, 0)
center: (0, 0)
center: (0, 0)
center: (0, 0)
11. Find the center and foci of the ellipse.
(y + 9)
(x + 5) 2
+
5
9
Ê
ˆ
A) center: ÁË 5, 9 ˜¯
B) center: ÊÁË −5, −9 ˆ˜¯
C) center: ÁÊË −5, −9 ˜ˆ¯
D) center: ÊÁË 5, 9 ˆ˜¯
____
vertices: (0, –2), (0, 2)
vertices: (–2, 0), (2, 0)
vertices: (0, –7), (0, 7)
vertices: (–7, 0), (7, 0)
2
foci: ÊÁË 5, 7 ˆ˜¯ , ÊÁË 5, 11 ˆ˜¯
foci: ÊÁË −5, −11 ˆ˜¯ , ÊÁË −5, −7 ˆ˜¯
foci: ÁÊË −7, −9 ˜ˆ¯ , ÁÊË −3, −9 ˜ˆ¯
foci: ÊÁË 3, −9 ˆ˜¯ , ÊÁË 7, −9 ˆ˜¯
12. Find the center and vertices of the ellipse.
2
2
4x + 9y − 24x + 72y + 144 = 0
A) center: ÁÊË −4, 3 ˜ˆ¯
B) center: ÊÁË −3, 4 ˆ˜¯
C) center: ÊÁË 3, −4 ˆ˜¯
D) center: ÊÁË 3, −4 ˆ˜¯
E) center: ÁÊË −3, 4 ˜ˆ¯
vertices: ÊÁË −7, 3 ˜ˆ¯ ,
vertices: ÊÁË −5, 4 ˆ˜¯ ,
vertices: ÊÁË 1, −4 ˆ˜¯ ,
vertices: ÊÁË 0, −4 ˆ˜¯ ,
vertices: ÁÊË −6, 4 ˜ˆ¯ ,
4
ÁÊË −1, 3 ˜ˆ¯
ÊÁ −1, 4 ˆ˜
Ë
¯
ÊÁ 5, −4 ˆ˜
Ë
¯
ÊÁ 6, −4 ˆ˜
Ë
¯
ÁÊË 0, 4 ˜ˆ¯
Name: ______________________
____
ID: A
13. Identify the graph of the following ellipse.
2
2
x + y =1
16
4
A)
C)
B)
____
14. Find the center and vertices of the hyperbola.
2
2
11x − 25y + 22x + 250y − 889 = 0
A) center: (1, –5), vertices: (1, –10), (1, 0)
B) center: (–1, 5), vertices: (–1, 0), (–1, 10)
C) center: (–1, 5), vertices: (–6, 5), (4,5)
D) center: (1,–5), vertices: (–4, –5), (6, –5)
5
Name: ______________________
____
15. Find the vertices and asymptotes of the hyperbola.
2
9y
− 16x
2
= 144
A) vertices: ÊÁË 0, ±4 ˆ˜¯
B)
vertices: ÊÁË 0, ±4 ˆ˜¯
C)
vertices: ÊÁË ±4, 0 ˆ˜¯
D) vertices: ÁÊË ±4, 0 ˜ˆ¯
____
ID: A
asymptote: y = ± 4 x
3
asymptote: y = ± 3 x
4
asymptote: y = ± 4 x
3
asymptote: y = ± 3 x
4
16. Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: ÊÁË 0, ±6 ˆ˜¯
A)
B)
y
2
y
2
foci: ÊÁË 0, ±7 ˆ˜¯
2
2
− x = 1
36
49
C)
2
x − y = 1
36
13
D)
2
x − y = 49
36
13
2
2
− x = 1
36
13
6
Name: ______________________
____
17. Find the graph of the following ellipse.
9x
____
2
2
+ 16y − 36x − 64y + -44 = 0
A)
C)
B)
D)
18. Write the equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,
7).
A)
B)
____
ID: A
2
2
x + y =1
49
33
2
2
x − y =1
33
49
C)
D)
2
2
x + y = −1
33
49
2
2
x + y =1
33
49
19. Find the center and vertices of the ellipse.
2
2
x + 9y + 16x − 54y + 136 = 0
A)
B)
C)
D)
E)
center: (3, –8)
center: (8, –3)
center: (–8, 3)
center: (–8, 3)
center: (8, –3)
vertices: (0, –8), (6, –8)
vertices: (7, –3), (9, –3)
vertices: (–9, 3), (–7, 3)
vertices: (–11, 3), (–5, 3)
vertices: (5, –3), (11, –3)
7
Name: ______________________
____
ID: A
20. Find the standard form of the equation of the ellipse with the following characteristics.
foci: ÊÁË ±4, 0 ˆ˜¯
major axis of length: 12
2
A)
2
x + y = 1
36
20
B)
2
x + y = 1
36
16
C)
2
x + y = 1
16
36
2
D)
2
y
x
+
= 1
144
16
E)
2
y
x
+
= 1
144
128
2
2
2
____
21. Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: (–2, –4), (–2, 6)
ÊÁ y − 1 ˆ˜ 2
2
Ë
¯
(x + 2)
−
=1
25
11
ÊÁ y + 1 ˆ˜ 2
2
Ë
¯
(x − 2)
−
=1
25
11
A)
B)
____
foci: (–2, –5), (–2, 7)
C)
D)
22. Graph the hyperbola.
9x
2
− 9y
2
= 81
A)
C)
B)
D)
8
ÊÁ y − 2 ˆ˜ 2
2
Ë
¯
(x + 1)
−
=1
11
25
ÊÁ y − 1 ˆ˜ 2
2
Ë
¯
(x + 2)
−
=1
25
36
Name: ______________________
____
ID: A
23. Identify the conic by writing the equation in standard form.
2
2
10y − 20x + 60y + 160x − 255 = 0
ÊÁ y − 3 ˆ˜ 2
2
Ë
¯
(x − 4)
A)
−
= 1; hyperbola
5
5
2
4
2
2
ÁÊË y + 3 ˜ˆ¯
(x − 4)
B)
−
= 1; hyperbola
5
5
2
4
2
ÊÁ y + 3 ˆ˜
2
Ë
¯
(x − 4)
C)
−
= 1; hyperbola
97
97
2
4
____
24. Identify the conic by writing the equation in standard form.
2
2
4x + 4y + 40x + 16y + 40 = 0
2
2
A) (x + 5) + ÊÁË y + 2 ˆ˜¯ = 19; circle
2
2
B) (x + 5) + ÊÁË y + 2 ˆ˜¯ = 39; circle
C)
(x + 5)
11
4
2
ÊÁ y + 2 ˆ˜ 2
Ë
¯
+
= 1; ellipse
11
4
9
ID: A
Conic Sections Practice Test
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
(2, −9), r = 1
C
B
D
A
E
D
A
2
x = 20y
D
B
D
A
C
A
B
B
D
D
A
A
C
B
A
1