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KEAM 2010 Math Paper
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© examsnet.com
Question : 35
Total: 120
The distance between the origin and the normal to the curve
y
=
e
2
x
+
x
2
at
x
=
0
is
2
2
√
3
2
√
5
1
2
1
√
5
Validate
Solution:
Given curve is
y
=
e
2
x
+
x
2
∴
x
=
0
⇒
y
=
1
⇒
d
y
d
x
=
2
e
2
x
+
2
x
=
2
(
e
2
x
+
x
)
∴
(
d
y
d
x
)
(
0
,
1
)
=
2
∴ Equation of normal at (0,1) is
y
−
1
=
−
1
2
(
x
−
0
)
⇒
2
y
+
x
=
2
∴ Required distance
=
|
−
2
√
2
2
+
1
2
|
=
|
−
2
√
5
|
=
2
√
5
© examsnet.com
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