Equations of Ellipses

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Kuta Software - Infinite Algebra 2
Name___________________________________
Writing Equations of Ellipses
Date________________ Period____
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 −
Co-vertices: (−1, 5), (−13, 5)
13 )
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)
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-1-
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)
91
10
Co-vertices: (12, 1), (6, 1)
y
26) Eccentricity =
6
4
2
−8
−6
−4
−2
2
4
6 x
−2
−4
−6
−8
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Writing Equations of Ellipses
Date________________ Period____
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
2) Vertices: (0, 6), (0, −6)
Co-vertices: (5, 0), (−5, 0)
2
2
x
y
+
=1
100 81
3) Vertices: (12, 0), (−12, 0)
Foci: (2 11, 0), (−2 11, 0)
2
4) Vertices: (14, 0), (−14, 0)
Foci: (3 19, 0), (−3 19, 0)
2
2
x
y
+
=1
144 100
+
( y − 5) 2
36
13 )
6) Foci: (7, 9), (−1, 9)
Co-vertices: (3, 12), (3, 6)
( x − 3) 2
=1
2
144
2
( y + 4) 2
+
( y + 5) 2
15
+
( x + 3) 2
=1
=1
196
+
81
( y + 4) 2
=1
16
14) Center: (7, −10)
Vertex: (−6, −10)
Co-vertex: (7, −17)
( x − 7) 2
=1
169
170
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( y − 7) 2
12) Center: (−3, −4)
Vertex: (6, −4)
Focus: (−3 − 65, −4)
144
( y − 8) 2
+
81
13) Center: (4, 8)
Vertex: (4, 8 − 170 )
Co-vertex: (4 − 15, 8)
( x − 4) 2
( x + 5) 2
4
36
2
10) Foci: (−5, 7 + 115 ), (−5, 7 − 115 )
Endpoints of minor axis: (4, 7), (−14, 7)
=1
11) Center: (6, −5)
Vertex: (6, 7)
Focus: (6, −5 − 6 3 )
( x − 6) 2
=1
9
x
y
+
=1
195 80
9) Foci: (7 + 2 35, −4), (7 − 2 35, −4)
Endpoints of minor axis: (7, −2), (7, −6)
+
( y − 9) 2
8) Foci: ( 115, 0), (− 115, 0)
Endpoints of major axis: ( 195, 0), (− 195, 0)
x
y
+
=1
81 64
( x − 7) 2
+
25
49
7) Foci: ( 17, 0), (− 17, 0)
Endpoints of major axis: (9, 0), (−9, 0)
2
2
x
y
+
=1
196 25
5) Foci: (−7, 5 + 13 ), (−7, 5 −
Co-vertices: (−1, 5), (−13, 5)
( x + 7) 2
2
x
y
+
=1
25 36
-1-
+
( y + 10) 2
=1
49
Worksheet by Kuta Software LLC
15) Center: (−3, 3)
Vertex: (−10, 3)
c 2 = 33
( x + 3) 2
+
16) Center: (1, −7)
Vertex: (1, 1)
c 2 = 55
( y − 3) 2
49
( x − 1) 2
=1
16
9
17) Center: (−9, 5)
Focus: (−9 + 2 14, 5)
Co-vertex: (−9, 10)
( x + 9) 2
+
( y − 5) 2
81
81
( x − 6) 2
=1
25
16
( x − 4) 2
+
( y + 8) 2
49
( y + 7) 2
x2
y2
+
=1
144
9
=1
81
+
64
( y − 7) 2
=1
121
24) Major axis is vertical
Center: (8, −2)
Major axis is 18 units long
Minor axis is 8 units long
( x − 8) 2
+
( y + 2) 2
16
25)
26) Eccentricity =
4
( x − 9) 2
2
9
−6
−4
−2
=1
81
91
10
Co-vertices: (12, 1), (6, 1)
y
6
−8
=1
81
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)
( x − 4) 2
=1
25
20) Center: (4, −8)
Height: 18
Width: 14
y2
+
=1
144
+
+
( y + 4) 2
49
21) Center: (9, −7)
a=9
b=4
Width: 8
( x − 9) 2
=1
64
18) Center: (6, −4)
Focus: (6 + 2 6, −4)
Co-vertex: (6, 1)
19) Center: (4, 0)
Focus: (4, 3 7 )
Width: 18
( x − 4) 2
+
( y + 7) 2
2
4
+
( y − 1) 2
=1
100
6 x
−2
−4
−6
−8
( x + 1) 2
36
+
( y + 1) 2
=1
25
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