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Tardigrade
Question
Mathematics
The eccentricity of an ellipse whose pair of a conjugate diameter are y=x and 3y=-2x is
Q. The eccentricity of an ellipse whose pair of a conjugate diameter are
y
=
x
and
3
y
=
−
2
x
is
1933
201
Jharkhand CECE
Jharkhand CECE 2012
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A
3
2
B
3
1
C
3
1
D
None of these
Solution:
Let the ellipse be
a
2
x
2
+
b
2
y
2
=
1
. Since,
y
=
x
and
3
y
=
−
2
x
is a pair of conjugate diameters. Therefore,
m
1
m
2
=
−
a
2
b
2
⇒
(
1
)
(
−
3
2
)
=
−
a
2
b
2
⇒
2
a
2
=
3
b
2
⇒
2
a
2
=
3
a
2
(
1
−
e
2
)
⇒
2
=
3
(
1
−
e
2
)
⇒
e
2
=
3
1
⇒
e
=
3
1