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The distance between the origin and the ...

The distance between the origin and the normal to the curve `y=e^(2x)+x^(2)` at `x=0` is

A

`2/(sqrt(3))`

B

`2/(sqrt(5))`

C

`2/(sqrt(7))`

D

`1/(sqrt(5))`

Text Solution

Verified by Experts

The correct Answer is:
B
`(dy)/(dx)=2e^(2x)+2ximplies((dy)/(dx))_(x=0)=2e^(@)+0=2`
Slope of normal `=-1/2` at `x=0,y=1`
Equation of normal `y-1=1/2(x-0)`
`impliesx+2y-2=0`
its distance from `(0,0)=2/(sqrt(5))`
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