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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Writing Equations of Ellipses
Use the information provided to write the standard form equation of each ellipse.
1) Vertices:
(
10, 0
)
,
(
−10, 0
)
Co-vertices:
(
0, 9
)
,
(
0, −9
)
2) Vertices:
(
0, 6
)
,
(
0, −6
)
Co-vertices:
(
5, 0
)
,
(
−5, 0
)
3) Vertices:
(
12, 0
)
,
(
−12, 0
)
Foci:
(
2 11, 0
)
,
(
−2 11, 0
)
4) Vertices:
(
14, 0
)
,
(
−14, 0
)
Foci:
(
3 19, 0
)
,
(
−3 19, 0
)
5) Foci:
(
−7,
5 + 13
)
,
(
−7,
5 −
13
)
Co-vertices:
(
−1, 5
)
,
(
−13, 5
)
6) Foci:
(
7, 9
)
,
(
−1, 9
)
Co-vertices:
(
3, 12
)
,
(
3, 6
)
7) Foci:
(
17, 0
)
,
(
− 17, 0
)
Endpoints of major axis:
(
9, 0
)
,
(
−9, 0
)
8) Foci:
(
115, 0
)
,
(
− 115, 0
)
Endpoints of major axis:
(
195, 0
)
,
(
− 195, 0
)
9) Foci:
(
7 +
2 35, −4
)
,
(
7 −
2 35, −4
)
Endpoints of minor axis:
(
7, −2
)
,
(
7, −6
)
10) Foci:
(
−5,
7 + 115
)
,
(
−5,
7 −
115
)
Endpoints of minor axis:
(
4, 7
)
,
(
−14, 7
)
11) Center:
(
6, −5
)
Vertex:
(
6, 7
)
Focus:
(
6,
−5 −
6 3
)
12) Center:
(
−3, −4
)
Vertex:
(
6, −4
)
Focus:
(
−3 −
65, −4
)
13) Center:
(
4, 8
)
Vertex:
(
4,
8 −
170
)
Co-vertex:
(
4 −
15, 8
)
14) Center:
(
7, −10
)
Vertex:
(
−6, −10
)
Co-vertex:
(
7, −17
)
-1-
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Worksheet by Kuta Software LLC
15) Center:
(
−3, 3
)
Vertex:
(
−10, 3
)
c
2
= 33
16) Center:
(
1, −7
)
Vertex:
(
1, 1
)
c
2
= 55
17) Center:
(
−9, 5
)
Focus:
(
−9 +
2 14, 5
)
Co-vertex:
(
−9, 10
)
18) Center:
(
6, −4
)
Focus:
(
6 +
2 6, −4
)
Co-vertex:
(
6, 1
)
19) Center:
(
4, 0
)
Focus:
(
4,
3 7
)
Width: 18
20) Center:
(
4, −8
)
Height: 18
Width: 14
21) Center:
(
9, −7
)
a
= 9
b
= 4
Width: 8
22) Center at origin
Focus:
(
3 15, 0
)
y-intercept:
(
0, 3
)
23) Endpoints of major axis:
(
4, 18
)
,
(
4, −4
)
Endpoints of minor axis:
(
12, 7
)
,
(
−4, 7
)
24) Major axis is vertical
Center:
(
8, −2
)
Major axis is 18 units long
Minor axis is 8 units long
25)
x
y
−8 −6 −4 −2 2 4 6
−8
−6
−4
−2
2
4
6
26) Eccentricity =
91
10
Co-vertices:
(
12, 1
)
,
(
6, 1
)
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Writing Equations of Ellipses
Use the information provided to write the standard form equation of each ellipse.
1) Vertices:
(
10, 0
)
,
(
−10, 0
)
Co-vertices:
(
0, 9
)
,
(
0, −9
)
x
2
100
+
y
2
81
= 1
2) Vertices:
(
0, 6
)
,
(
0, −6
)
Co-vertices:
(
5, 0
)
,
(
−5, 0
)
x
2
25
+
y
2
36
= 1
3) Vertices:
(
12, 0
)
,
(
−12, 0
)
Foci:
(
2 11, 0
)
,
(
−2 11, 0
)
x
2
144
+
y
2
100
= 1
4) Vertices:
(
14, 0
)
,
(
−14, 0
)
Foci:
(
3 19, 0
)
,
(
−3 19, 0
)
x
2
196
+
y
2
25
= 1
5) Foci:
(
−7,
5 + 13
)
,
(
−7,
5 −
13
)
Co-vertices:
(
−1, 5
)
,
(
−13, 5
)
(
x
+ 7
)
2
36
+
(
y
− 5
)
2
49
= 1
6) Foci:
(
7, 9
)
,
(
−1, 9
)
Co-vertices:
(
3, 12
)
,
(
3, 6
)
(
x
− 3
)
2
25
+
(
y
− 9
)
2
9
= 1
7) Foci:
(
17, 0
)
,
(
− 17, 0
)
Endpoints of major axis:
(
9, 0
)
,
(
−9, 0
)
x
2
81
+
y
2
64
= 1
8) Foci:
(
115, 0
)
,
(
− 115, 0
)
Endpoints of major axis:
(
195, 0
)
,
(
− 195, 0
)
x
2
195
+
y
2
80
= 1
9) Foci:
(
7 +
2 35, −4
)
,
(
7 −
2 35, −4
)
Endpoints of minor axis:
(
7, −2
)
,
(
7, −6
)
(
x
− 7
)
2
144
+
(
y
+ 4
)
2
4
= 1
10) Foci:
(
−5,
7 + 115
)
,
(
−5,
7 −
115
)
Endpoints of minor axis:
(
4, 7
)
,
(
−14, 7
)
(
x
+ 5
)
2
81
+
(
y
− 7
)
2
196
= 1
11) Center:
(
6, −5
)
Vertex:
(
6, 7
)
Focus:
(
6,
−5 −
6 3
)
(
x
− 6
)
2
36
+
(
y
+ 5
)
2
144
= 1
12) Center:
(
−3, −4
)
Vertex:
(
6, −4
)
Focus:
(
−3 −
65, −4
)
(
x
+ 3
)
2
81
+
(
y
+ 4
)
2
16
= 1
13) Center:
(
4, 8
)
Vertex:
(
4,
8 −
170
)
Co-vertex:
(
4 −
15, 8
)
(
x
− 4
)
2
15
+
(
y
− 8
)
2
170
= 1
14) Center:
(
7, −10
)
Vertex:
(
−6, −10
)
Co-vertex:
(
7, −17
)
(
x
− 7
)
2
169
+
(
y
+ 10
)
2
49
= 1
-1-
©
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Worksheet by Kuta Software LLC
15) Center:
(
−3, 3
)
Vertex:
(
−10, 3
)
c
2
= 33
(
x
+ 3
)
2
49
+
(
y
− 3
)
2
16
= 1
16) Center:
(
1, −7
)
Vertex:
(
1, 1
)
c
2
= 55
(
x
− 1
)
2
9
+
(
y
+ 7
)
2
64
= 1
17) Center:
(
−9, 5
)
Focus:
(
−9 +
2 14, 5
)
Co-vertex:
(
−9, 10
)
(
x
+ 9
)
2
81
+
(
y
− 5
)
2
25
= 1
18) Center:
(
6, −4
)
Focus:
(
6 +
2 6, −4
)
Co-vertex:
(
6, 1
)
(
x
− 6
)
2
49
+
(
y
+ 4
)
2
25
= 1
19) Center:
(
4, 0
)
Focus:
(
4,
3 7
)
Width: 18
(
x
− 4
)
2
81
+
y
2
144
= 1
20) Center:
(
4, −8
)
Height: 18
Width: 14
(
x
− 4
)
2
49
+
(
y
+ 8
)
2
81
= 1
21) Center:
(
9, −7
)
a
= 9
b
= 4
Width: 8
(
x
− 9
)
2
16
+
(
y
+ 7
)
2
81
= 1
22) Center at origin
Focus:
(
3 15, 0
)
y-intercept:
(
0, 3
)
x
2
144
+
y
2
9
= 1
23) Endpoints of major axis:
(
4, 18
)
,
(
4, −4
)
Endpoints of minor axis:
(
12, 7
)
,
(
−4, 7
)
(
x
− 4
)
2
64
+
(
y
− 7
)
2
121
= 1
24) Major axis is vertical
Center:
(
8, −2
)
Major axis is 18 units long
Minor axis is 8 units long
(
x
− 8
)
2
16
+
(
y
+ 2
)
2
81
= 1
25)
x
y
−8 −6 −4 −2 2 4 6
−8
−6
−4
−2
2
4
6
(
x
+ 1
)
2
36
+
(
y
+ 1
)
2
25
= 1
26) Eccentricity =
91
10
Co-vertices:
(
12, 1
)
,
(
6, 1
)
(
x
− 9
)
2
9
+
(
y
− 1
)
2
100
= 1
-2-
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