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JEE Main Math Class 11 Coordinate Geometry Part 1 Questions
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© examsnet.com
Question : 4
Total: 100
Let a and b respectively be the semi transverse and semi conjugate axes of a hyperbola whose eccentricity satisfies the equation
9
e
2
−
18
e
+
5
=
0
.
If
S
(
5
,
0
)
is a focus and
5
x
=
9
is the corresponding directrix of this hyperbola, then
a
2
−
b
2
is equal to :
[Online April 9, 2016]
-7
-5
5
7
Validate
Solution:
S
(
5
,
0
)
is focus
⇒
a
e
=
5
(focus) ––––– (a)
x
=
a
5
⇒
a
e
=
9
5
(directrix) ––––– (b)
(a)
&
(
b
)
⇒
a
2
=
9
(a)
(
a
)
⇒
(
e
)
=
5
3
b
2
=
a
2
(
e
2
−
1
)
⇒
b
2
=
16
a
2
−
b
2
=
9
−
16
=
−
7
© examsnet.com
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