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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Classifying Conic Sections
Classify each conic section.
1)
x
2
+
y
2
= 30 2)
x
2
+
y
2
= 36
3)
x
2
9
+
y
2
16
= 1
4)
x =
y
2
5)
x =
(
y + 4
)
2
− 2
6)
y
2
25
−
x
2
25
= 1
7)
y =
(
x − 1
)
2
+ 3
8)
(
x − 1
)
2
+
y
2
25
= 1
Classify each conic section and write its equation in standard form.
9)
−
x
2
+ 10
x +
y − 21 = 0 10)
−2
y
2
+
x − 20
y − 49 = 0
11)
x
2
+ 2
x +
y − 1 = 0 12)
x
2
+
y
2
+ 6
x − 2
y + 9 = 0
13)
x
2
−
y
2
− 2
x − 8 = 0 14)
3
x
2
+ 30
x +
y + 79 = 0
15)
−9
x
2
+
y
2
− 72
x − 153 = 0 16)
−
y
2
+
x + 8
y − 17 = 0
-1-
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Worksheet by Kuta Software LLC
Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas,
identify the vertex and focus. For circles, identify the center and radius. For ellipses and hyperbolas
identify the center, vertices, and foci.
17)
−2
y
2
+
x − 4
y + 1 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
18)
−25
x
2
+
y
2
− 100
x − 125 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
19)
4
x
2
+ 4
y
2
− 20
x − 32
y + 81 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-2-
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Worksheet by Kuta Software LLC
20)
9
x
2
+ 4
y
2
− 54
x − 8
y − 59 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
21)
−9
x
2
+ 25
y
2
− 100
y − 125 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
22)
y
2
+
x + 10
y + 26 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-3-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Classifying Conic Sections
Classify each conic section.
1)
x
2
+
y
2
= 30
Circle
2)
x
2
+
y
2
= 36
Circle
3)
x
2
9
+
y
2
16
= 1
Ellipse
4)
x =
y
2
Parabola
5)
x =
(
y + 4
)
2
− 2
Parabola
6)
y
2
25
−
x
2
25
= 1
Hyperbola
7)
y =
(
x − 1
)
2
+ 3
Parabola
8)
(
x − 1
)
2
+
y
2
25
= 1
Ellipse
Classify each conic section and write its equation in standard form.
9)
−
x
2
+ 10
x +
y − 21 = 0
Parabola
y =
(
x − 5
)
2
− 4
10)
−2
y
2
+
x − 20
y − 49 = 0
Parabola
x =
2
(
y + 5
)
2
− 1
11)
x
2
+ 2
x +
y − 1 = 0
Parabola
y =
−
(
x + 1
)
2
+ 2
12)
x
2
+
y
2
+ 6
x − 2
y + 9 = 0
Circle
(
x + 3
)
2
+
(
y − 1
)
2
= 1
13)
x
2
−
y
2
− 2
x − 8 = 0
Hyperbola
(
x − 1
)
2
9
−
y
2
9
= 1
14)
3
x
2
+ 30
x +
y + 79 = 0
Parabola
y =
−3
(
x + 5
)
2
− 4
15)
−9
x
2
+
y
2
− 72
x − 153 = 0
Hyperbola
y
2
9
−
(
x + 4
)
2
= 1
16)
−
y
2
+
x + 8
y − 17 = 0
Parabola
x =
(
y − 4
)
2
+ 1
-1-
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Worksheet by Kuta Software LLC
Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas,
identify the vertex and focus. For circles, identify the center and radius. For ellipses and hyperbolas
identify the center, vertices, and foci.
17)
−2
y
2
+
x − 4
y + 1 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Parabola
x =
2
(
y + 1
)
2
− 3
Vertex:
(
−3, −1
)
Focus:
(
−
23
8
, −1
)
18)
−25
x
2
+
y
2
− 100
x − 125 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Hyperbola
y
2
25
−
(
x + 2
)
2
= 1
Center:
(
−2, 0
)
Vertices:
(
−2, 5
)
,
(
−2, −5
)
Foci:
(
−2, 26
)
,
(
−2,
− 26
)
19)
4
x
2
+ 4
y
2
− 20
x − 32
y + 81 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Circle
(
x −
5
2
)
2
+
(
y − 4
)
2
= 2
Center:
(
5
2
, 4
)
Radius: 2
-2-
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Worksheet by Kuta Software LLC
20)
9
x
2
+ 4
y
2
− 54
x − 8
y − 59 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Ellipse
(
x − 3
)
2
16
+
(
y − 1
)
2
36
= 1
Center:
(
3, 1
)
Vertices:
(
3, 7
)
,
(
3, −5
)
Foci:
(
3,
1 +
2 5
)
,
(
3,
1 −
2 5
)
21)
−9
x
2
+ 25
y
2
− 100
y − 125 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Hyperbola
(
y − 2
)
2
9
−
x
2
25
= 1
Center:
(
0, 2
)
Vertices:
(
0, 5
)
,
(
0, −1
)
Foci:
(
0,
2 + 34
)
,
(
0,
2 −
34
)
22)
y
2
+
x + 10
y + 26 = 0
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Parabola
x =
−
(
y + 5
)
2
− 1
Vertex:
(
−1, −5
)
Focus:
(
−
5
4
, −5
)
-3-
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