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JEE Main 2017 Solved Paper Solved Paper
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© examsnet.com
Question : 40
Total: 90
A hyperbola passes through the point
P
(
√
2
,
√
3
)
and has foci at
(
±
2
,
0
)
. Then the tangent to this hyperbola at P also passes through the point :
(
−
√
2
,
−
√
3
)
(
3
√
2
,
2
√
3
)
(
2
√
2
,
3
√
3
)
(
√
3
,
√
2
)
Validate
Solution:
Equation of hyperbola is
x
2
a
2
−
y
2
b
2
=
1
foci is
(
±
2
,
0
)
hence
a
e
=
2
,
⇒
a
2
e
2
=
4
b
2
=
a
2
(
e
2
−
1
)
∴
a
2
+
b
2
=
4
......(1)
Hyperbola passes through
(
√
2
,
√
3
)
∴
2
a
2
−
3
b
2
=
1
......(2)
On solving (1) and (2)
a
2
=
8
(is rejected) and
a
2
=
1
and
b
2
=
3
∴
x
2
1
−
y
2
3
=
1
Equation of tangent id
√
2
x
1
−
√
3
y
3
=
1
Hence
(
2
√
2
,
3
√
3
)
satisfy it
© examsnet.com
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