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JEE Main Math Class 11 Coordinate Geometry Part 3 Questions
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© examsnet.com
Question : 4
Total: 100
Let
P
Q
be a focal chord of the parabola
y
2
=
4
x
such that it subtends an angle of
π
2
at the point
(
3
,
0
)
. Let the line segment
P
Q
be also a focal chord of the ellipse
E
:
x
2
a
2
+
y
2
b
2
=
1
,
a
2
>
b
2
. If e is the eccentricity of the ellipse
E
, then the value of
1
e
2
is equal to:
[29-Jun-2022-Shift-1]
1
+
√
2
3
+
2
√
2
1
+
2
√
3
4
+
5
√
3
Validate
Solution:
As
∠
P
R
Q
=
π
2
(
2
t
3
−
1
t
2
)
⋅
(
−
2
t
3
−
t
2
)
=
−
1
⇒
t
=
±
1
∴
P
≡
(
1
,
2
)
&
Q
(
1
,
−
2
)
∴
for ellipse
1
a
2
+
4
b
2
=
1
and
a
e
=
1
⇒
1
a
2
+
4
a
2
(
1
−
e
2
)
=
1
⇒
1
+
4
(
1
−
e
2
)
=
1
e
2
⇒
(
5
−
e
2
)
e
2
=
1
−
e
2
⇒
e
4
−
6
e
2
+
1
=
0
⇒
e
2
=
1
3
−
2
√
2
⇒
1
e
2
=
3
+
2
√
2
© examsnet.com
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