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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing and Properties of Ellipses
Identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of each.
1)
x
2
49
+
y
2
169
= 1 2)
x
2
36
+
y
2
16
= 1
3)
x
2
95
+
y
2
30
= 1 4)
x
2
169
+
y
2
64
= 1
5)
x
2
64
+
(
y
− 6
)
2
121
= 1 6)
(
x
+ 5
)
2
81
+
(
y
− 1
)
2
144
= 1
-1-
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Worksheet by Kuta Software LLC
7)
(
x
− 3
)
2
49
+
(
y
− 9
)
2
4
= 1 8)
x
2
64
+
(
y
− 8
)
2
9
= 1
Graph each equation.
9)
x
2
4
+
y
2
9
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
10)
x
2
49
+
y
2
= 1
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
11)
x
2
36
+
y
2
25
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
12)
x
2
9
+
y
2
49
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
13)
x
2
49
+
(
y
− 3
)
2
16
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
14)
(
x
− 1
)
2
4
+
y
2
49
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
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Worksheet by Kuta Software LLC
15)
x
2
49
+
(
y
− 1
)
2
9
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
16)
(
x
+ 5
)
2
+
y
2
49
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Identify the length of the major axis, length of the minor axis, length of the latus rectum, and eccentricity of
each.
17)
−16
y
+ 52 =
−2
x
2
− 8
x
−
y
2
18)
4
y
2
− 338
x
+ 32
y
=
−169
x
2
+ 443
19)
(
x
+ 4
)
2
4
+
(
y
+ 9
)
2
64
= 1
20)
126
y
+ 9
y
2
− 8
x
− 131 = −4
x
2
-4-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing and Properties of Ellipses
Identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of each.
1)
x
2
49
+
y
2
169
= 1
Center:
(
0, 0
)
Vertices:
(
0, 13
)
,
(
0, −13
)
Co-vertices:
(
7, 0
)
,
(
−7, 0
)
Foci:
(
0,
2 30
)
,
(
0,
−2 30
)
Major Axis: 26 units
Minor Axis: 14 units
2)
x
2
36
+
y
2
16
= 1
Center:
(
0, 0
)
Vertices:
(
6, 0
)
,
(
−6, 0
)
Co-vertices:
(
0, 4
)
,
(
0, −4
)
Foci:
(
2 5, 0
)
,
(
−2 5, 0
)
Major Axis: 12 units
Minor Axis: 8
units
3)
x
2
95
+
y
2
30
= 1
Center:
(
0, 0
)
Vertices:
(
95, 0
)
,
(
− 95, 0
)
Co-vertices:
(
0, 30
)
,
(
0,
− 30
)
Foci:
(
65, 0
)
,
(
− 65, 0
)
Major Axis:
2 95 units
Minor Axis:
2 30 units
4)
x
2
169
+
y
2
64
= 1
Center:
(
0, 0
)
Vertices:
(
13, 0
)
,
(
−13, 0
)
Co-vertices:
(
0, 8
)
,
(
0, −8
)
Foci:
(
105, 0
)
,
(
− 105, 0
)
Major Axis: 26 units
Minor Axis: 16
units
5)
x
2
64
+
(
y
− 6
)
2
121
= 1
Center:
(
0, 6
)
Vertices:
(
0, 17
)
,
(
0, −5
)
Co-vertices:
(
8, 6
)
,
(
−8, 6
)
Foci:
(
0,
6 + 57
)
,
(
0,
6 −
57
)
Major Axis: 22 units
Minor Axis: 16 units
6)
(
x
+ 5
)
2
81
+
(
y
− 1
)
2
144
= 1
Center:
(
−5, 1
)
Vertices:
(
−5, 13
)
,
(
−5, −11
)
Co-vertices:
(
4, 1
)
,
(
−14, 1
)
Foci:
(
−5,
1 +
3 7
)
,
(
−5,
1 −
3 7
)
Major Axis: 24 units
Minor Axis: 18
units
-1-
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Worksheet by Kuta Software LLC
7)
(
x
− 3
)
2
49
+
(
y
− 9
)
2
4
= 1
Center:
(
3, 9
)
Vertices:
(
10, 9
)
,
(
−4, 9
)
Co-vertices:
(
3, 11
)
,
(
3, 7
)
Foci:
(
3 +
3 5, 9
)
,
(
3 −
3 5, 9
)
Major Axis: 14 units
Minor Axis: 4 units
8)
x
2
64
+
(
y
− 8
)
2
9
= 1
Center:
(
0, 8
)
Vertices:
(
8, 8
)
,
(
−8, 8
)
Co-vertices:
(
0, 11
)
,
(
0, 5
)
Foci:
(
55, 8
)
,
(
− 55, 8
)
Major Axis: 16 units
Minor Axis: 6
units
Graph each equation.
9)
x
2
4
+
y
2
9
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
10)
x
2
49
+
y
2
= 1
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
11)
x
2
36
+
y
2
25
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
12)
x
2
9
+
y
2
49
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
13)
x
2
49
+
(
y
− 3
)
2
16
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
14)
(
x
− 1
)
2
4
+
y
2
49
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
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Worksheet by Kuta Software LLC
15)
x
2
49
+
(
y
− 1
)
2
9
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
16)
(
x
+ 5
)
2
+
y
2
49
= 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Identify the length of the major axis, length of the minor axis, length of the latus rectum, and eccentricity of
each.
17)
−16
y
+ 52 =
−2
x
2
− 8
x
−
y
2
Major Axis:
4 5 units
Minor Axis:
2 10 units
Latus Rectum:
2 5 units
Eccentricity:
2
2
≈ 0.707
18)
4
y
2
− 338
x
+ 32
y
=
−169
x
2
+ 443
Major Axis: 26 units
Minor Axis: 4 units
Latus Rectum:
8
13
units
Eccentricity:
165
13
≈ 0.988
19)
(
x
+ 4
)
2
4
+
(
y
+ 9
)
2
64
= 1
Major Axis: 16 units
Minor Axis: 4 units
Latus Rectum: 1 unit
Eccentricity:
15
4
≈ 0.968
20)
126
y
+ 9
y
2
− 8
x
− 131 = −4
x
2
Major Axis: 24 units
Minor Axis: 16 units
Latus Rectum:
32
3
units
Eccentricity:
5
3
≈ 0.745
-4-
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