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The point on the curve y^(2)=x where tan...

The point on the curve `y^(2)=x` where tangent makes `45^(@)` angle with x-axis, is

A

`(1/4,1/2)`

B

`(1/2,1/4)`

C

`(1/2,-1/2)`

D

`(1/2,1/2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `y^(2)=x`…………i
`implies2y(dy)/(dx)=1`
`implies(dy)/(dx)=1/(2y)=` slope
Also, given slope of curve
`=tan 45^(@)=1`
`=1/(2y)=1`
`impliesy=1/2`
Then, from Eq. (i) `x=1/4`
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