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NIMCET 2015 Question Paper with solutions
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© examsnet.com
Question : 12
Total: 120
The foci of the ellipse
x
2
16
+
y
2
b
2
= 1 and the hyperbola
x
2
144
−
y
2
81
=
1
25
coincide, then the value of
b
2
is :
1
5
7
9
Validate
Solution:
The foci of the ellipse
x
2
16
+
y
2
b
2
=
1
and the hyperbola
x
2
144
−
y
2
81
=
1
25
coincide
∴ Foci of the ellipse and hyperbola lie on X-axis
Foci of the ellipse
=
√
16
−
b
2
and foci of the hyperbola
=
√
144
25
+
81
25
Foci of the ellipse and hyperbola coincide
∴
√
16
−
b
2
=
√
144
25
+
81
25
Squaring both sides,
⇒
16
−
b
2
=
225
25
⇒
b
2
=
16
−
9
=
7
© examsnet.com
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