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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 20
Total: 71
An ellipse has
O
B
as semi minor axis,
F
and
F
its foci and the angle
F
B
F
′
is a right angle. Then the eccentricity of the ellipse is
1
√
2
1
2
1
4
1
√
3
Validate
Solution:
as
∠
F
B
F
′
=
90
∘
⇒
F
B
2
+
F
′
B
2
=
F
F
′
2
∴
(
√
a
2
e
2
+
b
2
)
2
+
(
√
a
2
e
2
+
b
2
)
=
(
2
a
e
)
2
⇒
2
(
a
2
e
2
+
b
2
)
=
4
a
2
e
2
⇒
e
2
=
b
2
a
2
Also
e
2
=
1
−
b
2
∕
a
2
=
1
−
e
2
⇒
2
e
2
=
1
,
e
=
1
√
2
© examsnet.com
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