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JEE Main Math Class 11 Coordinate Geometry Part 4 Questions
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© examsnet.com
Question : 27
Total: 100
If the line
x
−
1
=
0
is a directrix of the hyperbola
k
x
2
−
y
2
=
6
, then the hyperbola passes through the point
[26-Jul-2022-Shift-2]
(
−
2
√
5
,
6
)
(
−
√
5
,
3
)
(
√
5
,
−
2
)
(
2
√
5
,
3
√
6
)
Validate
Solution:
Given hyperbola :
x
2
6
∕
k
−
y
2
6
=
1
Eccentricity
=
e
=
√
1
+
6
6
∕
k
=
√
1
+
k
Directrices :
x
=
±
a
e
⇒
x
=
±
√
6
√
k
√
k
+
1
As given :
√
6
√
k
√
k
+
1
=
1
⇒
k
=
2
Here hyperbola is
x
2
3
−
y
2
6
=
1
Checking the option gives
(
√
5
,
−
2
)
satisfies it.
© examsnet.com
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