©
a
4
2
U
0
X
1
j
5
v
y
K
p
u
1
t
k
a
0
m
S
R
o
4
f
l
t
W
w
V
a
f
r
a
e
a
T
L
m
L
0
C
M
.
A
p
J
A
V
l
i
l
w
Z
r
m
i
9
g
z
h
v
t
H
s
m
d
r
l
e
K
s
p
e
d
r
n
v
h
e
O
d
x
.
a
5
3
M
v
a
C
d
P
e
D
b
w
X
i
A
t
a
h
o
g
I
k
n
H
f
w
i
l
n
5
i
Q
t
g
e
1
h
A
G
l
d
g
T
e
J
b
Z
r
E
a
L
I
2
n
.
B
Worksheet by Kuta Software LLC
©
u
7
2
B
0
x
1
6
5
6
D
K
R
u
Q
t
7
a
x
F
S
s
o
X
f
U
t
s
w
X
a
C
r
2
e
U
L
L
p
L
N
C
5
.
f
Y
z
A
P
l
a
l
R
7
r
z
i
C
g
r
h
s
t
6
s
n
f
r
e
e
3
s
i
e
9
r
W
v
9
e
0
d
j
.
6
Math Analysis Honors - Conic Sections Review
Use the information provided to write the standard
form equation of each circle.
1) Center:
(
2, −13
)
Point on Circle:
(
3, −18
)
Use the information provided to write the standard form equation of each ellipse.
2) Vertices:
(
19, 5
)
,
(
1, 5
)
Foci:
(
10 + 65, 5
)
,
(
10 −
65, 5
)
3) Endpoints of major axis:
(
13, 3
)
,
(
−9, 3
)
Endpoints of minor axis:
(
2, 9
)
,
(
2, −3
)
4) Minor axis is vertical
Center:
(
−7, 8
)
Major axis is 20 units long
Minor axis is 18 units long
Use the information provided to write the standard form equation of each hyperbola.
5) Vertices:
(
−5, −7
)
,
(
−15, −7
)
Foci:
(
3, −7
)
,
(
−23, −7
)
6) Foci:
(
13, −3
)
,
(
−13, −3
)
Asymptotes:
y =
12
5
x − 3
y =
−
12
5
x − 3
Use the information provided to write the vertex form equation of each parabola.
7) Vertex:
(
10, −8
)
, Focus:
(
41
4
, −8
)
8) Vertex:
(
−4, −1
)
, Directrix:
x =
−
17
4
-1-
©
3
V
2
g
0
l
1
i
5
X
p
K
j
u
4
t
4
a
s
L
S
Z
o
u
f
3
t
M
w
v
a
t
r
j
e
V
v
L
G
L
c
C
j
.
e
z
p
A
U
l
n
l
3
w
r
v
i
e
g
2
h
f
t
d
s
g
S
r
h
e
p
s
i
e
i
r
5
v
3
e
m
d
E
.
G
6
G
M
H
a
V
d
B
e
3
c
w
Z
i
Q
t
4
h
J
r
I
j
n
k
f
f
i
l
n
V
i
c
t
j
e
H
T
A
5
l
D
g
8
e
n
b
z
r
2
a
D
K
2
J
.
v
Worksheet by Kuta Software LLC
Identify the center and radius of each. Then sketch
the graph.
9)
(
x + 4
)
2
+
(
y + 3
)
2
= 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Identify the vertices and foci of each. Then sketch
the graph.
10)
(
x + 2
)
2
16
+
(
y + 3
)
2
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Identify the vertices, foci, and asymptotes of each.
Then sketch the graph.
11)
(
x − 3
)
2
4
−
(
y + 1
)
2
16
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Identify the vertex, focus, axis of symmetry, and
directrix of each. Then sketch the graph.
12)
−2
(
y + 5
)
=
(
x + 6
)
2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Classify each conic section and write its equation in standard form.
13)
x
2
+
y
2
+ 4
x + 8
y + 16 = 0 14)
x
2
+
y
2
− 8
y + 8 = 0
15)
−2
x
2
− 8
x +
y − 3 = 0 16)
3
x
2
+ 2
y
2
− 6
x − 87 = 0
17)
−3
x
2
+ 18
x +
y − 22 = 0 18)
x
2
− 9
y
2
+ 4
x − 54
y − 86 = 0
-2-
©
T
U
2
K
0
9
1
j
5
U
5
K
5
u
j
t
p
a
2
u
S
L
o
n
f
1
t
F
w
d
a
J
r
U
e
W
8
L
u
L
B
C
o
.
e
1
1
A
B
l
K
l
p
S
r
j
i
p
g
a
h
x
t
T
s
t
8
r
q
e
V
s
0
e
6
r
m
v
e
e
b
d
C
.
w
O
a
M
T
a
D
d
j
e
W
W
w
c
i
c
t
Y
h
M
Y
I
1
n
w
f
1
i
y
n
R
i
A
t
m
e
G
F
A
d
l
Q
g
r
e
N
b
1
r
8
a
A
B
2
v
.
n
Worksheet by Kuta Software LLC
-3-
Answers to
1)
(
x − 2
)
2
+
(
y + 13
)
2
= 26
2)
(
x − 10
)
2
81
+
(
y − 5
)
2
16
= 1 3)
(
x − 2
)
2
121
+
(
y − 3
)
2
36
= 1
4)
(
x + 7
)
2
100
+
(
y − 8
)
2
81
= 1 5)
(
x + 10
)
2
25
−
(
y + 7
)
2
144
= 1 6)
x
2
25
−
(
y + 3
)
2
144
= 1
7)
x =
(
y + 8
)
2
+ 10 8)
x =
(
y + 1
)
2
− 4
9)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Center:
(
−4, −3
)
Radius: 2
10)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertices:
(
2, −3
)
(
−6, −3
)
Foci:
(
−2 + 15 , −3
)
(
−2 −
15 , −3
)
11)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertices:
(
5, −1
)
(
1, −1
)
Foci:
(
3 +
2 5 , −1
)
(
3 −
2 5 , −1
)
Asym.:
y =
2
x − 7
y =
−2
x + 5
12)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
−6, −5
)
Focus:
(
−6,
−
11
2
)
Axis of Sym.:
x = −6
Directrix:
y =
−
9
2
13) Circle
(
x + 2
)
2
+
(
y + 4
)
2
= 4
14) Circle
x
2
+
(
y − 4
)
2
= 8
15) Parabola
y =
2
(
x + 2
)
2
− 5
16) Ellipse
(
x − 1
)
2
30
+
y
2
45
= 1
17) Parabola
y =
3
(
x − 3
)
2
− 5
18) Hyperbola
(
x + 2
)
2
9
−
(
y + 3
)
2
= 1