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Byju's Answer
Standard XII
Mathematics
Definition of Ellipse
The eccentric...
Question
The eccentricity of the ellipse
x
2
+
4
y
2
+
2
x
+
16
y
+
13
=
0
is
A
√
3
2
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B
1
2
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C
1
√
3
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D
1
√
2
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Solution
The correct option is
D
√
3
2
(
x
2
+
2
x
)
+
4
(
y
2
+
4
y
)
+
13
=
0
⇒
(
x
2
+
2
x
+
1
)
+
4
(
y
2
+
4
y
+
4
)
=
4
⇒
(
x
+
1
)
2
+
4
(
y
+
2
)
2
=
4
⇒
(
x
+
2
)
2
4
+
(
y
+
2
)
2
1
=
1
Hence eccentricity
=
√
1
−
1
4
=
√
3
2
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0
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