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NIMCET 2015 Question Paper with solutions
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© examsnet.com
Question : 5
Total: 120
If 3x + 4y + K=0 is tangent to the hyperbola
9
x
2
–
16
y
2
= 144, then the value of K is;
0
1
–1
–3
Validate
Solution:
We have,
3
x
+
4
y
+
k
=
0
is tangent of the hyperbola
9
x
2
−
16
y
2
=
144
Equation of hyperbola is
9
x
2
−
16
y
2
=
144
⇒
x
2
16
−
y
2
9
=
1
Equation of tangent is
3
x
+
4
y
+
k
=
0
We know that,
y
=
m
x
+
c
touches the hyperbola.
x
2
a
2
−
y
2
b
2
=
1
if
c
2
=
a
2
m
2
−
b
2
∴
(
−
k
4
)
2
=
16
(
−
3
4
)
2
−
9
⇒
k
2
16
=
9
−
9
⇒
k
=
0
© examsnet.com
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