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JEE Main Math Class 11 Coordinate Geometry Part 3 Questions
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© examsnet.com
Question : 3
Total: 100
Let the eccentricity of an ellipse
x
2
a
2
+
y
2
b
2
=
1
,
a
>
b
, be
1
4
. If this ellipse passes through the point
(
−
4
√
2
5
,
3
)
, then
a
2
+
b
2
is equal to :
[27-Jun-2022-Shift-1]
29
31
32
34
Validate
Solution:
x
2
a
2
+
y
2
b
2
=
1
⇒
(
−
4
√
2
5
)
2
a
2
+
32
b
2
=
1
⇒
32
5
a
2
+
9
b
2
=
1
.
.
.
.
(i)
a
2
(
1
−
e
2
)
=
b
2
a
2
(
1
−
1
16
)
=
b
2
15
a
2
=
16
b
2
⇒
a
2
=
16
b
2
15
From (i)
6
b
2
+
9
b
2
=
1
⇒
b
2
=
15
&
a
2
=
16
a
2
+
b
2
=
15
+
16
=
31
© examsnet.com
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