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JEE Main Math Class 11 Coordinate Geometry Part 6 Questions
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© examsnet.com
Question : 13
Total: 33
Consider a hyperbola
H
having centre at the origin and foci and the
x
-axis. Let
C
1
be the circle touching the hyperbola
H
and having the centre at the origin. Let
C
2
be the circle touching the hyperbola
H
at its vertex and having the centre at one of its foci. If areas (in sq. units) of
C
1
and
C
2
are
36
π
and
4
π
, respectively, then the length (in units) of latus rectum of
H
is
[4 Apr 2024 Shift 2]
28
3
14
3
10
3
11
3
Validate
Solution:
👈: Video Solution
Let
H
:
x
2
a
2
−
y
2
b
2
=
1
(
b
2
=
a
2
(
e
2
−
1
)
)
∴
eq
n
of
C
1
=
x
2
+
y
2
=
a
2
Ar.
=
36
π
π
a
2
=
36
π
a
=
6
Now radius of
C
2
can be
a
(
e
−
1
)
or a(e +1
)
for
r
=
a
(
e
−
1
)
for
r
=
a
(
e
+
1
)
Ar.
=
4
π
π
r
2
=
4
π
π
a
2
(
e
−
1
)
2
=
4
π
a
2
(
e
+
1
)
2
=
4
36
π
(
e
−
1
)
2
=
4
π
36
(
e
+
1
)
2
=
4
e
−
1
=
1
3
e
+
1
=
1
3
e
=
4
3
−
2
3
Not possible
∴
b
2
=
36
(
16
9
−
1
)
=
28
∴
LR
=
2
b
2
a
=
2
×
28
6
=
28
3
© examsnet.com
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