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Manipal Entrance Test 2014 Math Paper
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© examsnet.com
Question : 4
Total: 80
The common tangent of the parabolas
y
2
=
4
x
and
x
2
=
−
8
y
is
y = x + 2
y = x - 2
y = 2x + 3
None of these
Validate
Solution:
The equation of the tangent to parabola
y
2
=
4
x
is
y
=
m
x
+
1
m
This is also the tangent to parabola
x
2
=
−
8
y
∴
x
2
=
−
8
(
m
x
+
1
m
)
⇒
m
x
2
+
8
m
2
x
+
8
=
0
It has equal roots, if
64
m
4
=
32
m
[
∵
b
2
=
4
a
c
∵
]
m
3
=
1
2
⇒
m
=
1
3
√
2
Hence, equation of the tangent is
y
=
1
3
√
2
x
+
3
√
2
.
© examsnet.com
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