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Section:
Mathematics
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© examsnet.com
Question : 62
Total: 102
Let
E
1
:
x
2
a
2
+
y
2
b
2
=
1
,
a
>
b
.
Let
E
2
be another ellipse such that it touches the end points of major axis of
E
1
and the foci of
E
2
are the end points of minor axis of
E
1
. If
E
1
and
E
2
have same eccentricities, then its value is:
[22 Jul 2021 Shift 2]
−
1
+
√
5
2
−
1
+
√
8
2
−
1
+
√
3
2
−
1
+
√
6
2
Validate
Solution:
e
2
=
1
−
b
2
a
2
e
2
=
1
−
a
2
c
2
⇒
b
2
a
2
=
a
2
c
2
⇒
c
2
=
a
4
b
2
⇒
c
=
a
2
b
Also
b
=
c
e
⇒
c
=
b
e
b
e
=
a
2
b
⇒
e
=
b
2
a
2
=
1
−
e
2
⇒
e
2
+
e
−
1
=
0
⇒
e
=
−
1
+
√
5
2
© examsnet.com
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