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Standard XII
Mathematics
Eccentricity
If the latus-...
Question
If the latus-rectum of an ellipse be equal to half of its minor axis, then its eccentricity is
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Solution
Given: Length of latus-rectum is equal to half of minor axis.
⇒
2
b
2
a
=
b
⇒
b
a
=
1
2
[
∵
b
≠
0
]
⇒
b
2
a
2
=
1
4
⇒
1
−
b
2
a
2
=
3
4
⇒
e
2
=
3
4
∴
e
=
√
3
2
[
∵
e
>
0
]
Hence, the eccentricity is
e
=
√
3
2
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