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JEE Main Math Class 11 Coordinate Geometry Part 5 Questions
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© examsnet.com
Question : 30
Total: 100
Let
P
be a parabola with vertex
(
2
,
3
)
and directrix
2
x
+
y
=
6
. Let an ellipse
E
:
x
2
a
2
+
y
2
b
2
=
1
,
a
>
b
of eccentricity
1
√
2
pass through the focus of the parabola
P
. Then the square of the length of the latus rectum of
E
, is
[31-Jan-2024 Shift 2]
385
8
347
8
512
25
656
25
Validate
Solution:
👈: Video Solution
Slope of axis
=
1
2
y
−
3
=
1
2
(
x
−
2
)
⇒
2
y
−
6
=
x
−
2
⇒
2
y
−
x
−
4
=
0
2
x
+
y
−
6
=
0
4
x
+
2
y
−
12
=
0
α
+
1.6
=
4
⇒
α
=
2.4
β
+
2.8
=
6
⇒
β
=
3.2
Ellipse passes through
(
2.4
,
3.2
)
⇒
(
24
10
)
2
a
2
+
(
32
10
)
2
b
2
=
1
..............(1)
Also
1
−
b
2
a
2
=
1
2
=
b
2
a
2
=
1
2
⇒
a
2
=
2
b
2
Put in (1)
⇒
b
2
=
328
25
⇒
(
2
b
2
a
)
2
=
4
b
2
a
2
×
b
2
=
4
×
1
2
×
328
25
=
656
25
© examsnet.com
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