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Standard XII
Mathematics
Eccentricity
If the latus ...
Question
If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.
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Solution
According to given,
2
b
2
a
=
b
⇒
2
b
=
a
⇒
b
=
a
2
We know that
c
2
=
a
2
−
b
2
=
a
2
−
a
2
4
=
4
a
2
−
a
2
4
=
3
a
2
4
⇒
c
2
a
2
=
3
4
⇒
c
a
=
√
3
2
Hence, the eccentricity of the ellipse
=
√
3
2
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