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JEE Main Math Class 11 Coordinate Geometry Part 2 Questions
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© examsnet.com
Question : 8
Total: 100
If
3
x
+
4
y
=
12
√
2
is
a
tangent to the ellipse
x
2
a
2
+
y
2
9
=
1
for some
a
∈
R
,
then the distance between the foci of the ellipse is:
[Jan. 7, 2020 (II)]
2
√
7
4
2
√
5
2
√
2
Validate
Solution:
3
x
+
4
y
=
12
√
2
⇒
4
y
=
−
3
x
+
12
√
2
⇒
y
=
−
3
4
x
+
3
√
2
Now, condition of tangency,
c
2
=
a
2
m
2
+
b
2
18
=
a
2
⋅
9
16
+
9
⇒
a
2
⋅
9
16
=
9
⇒
a
2
=
16
⇒
a
=
4
Eccentricity
e
=
√
1
−
b
2
a
2
=
√
1
−
9
16
=
√
7
4
∴
a
e
=
√
7
4
⋅
4
=
√
7
∴ Focus are
(
±
√
7
,
0
)
∴ Distance between foci of ellipse
=
2
√
7
© examsnet.com
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