The point of the curve `y^(2)=2(x-3)` at which the normal is parallel to the line `y-2x+1=0` is

Options

A. `(5,2)`
B. `(1/2,-2)`
C. `(5,-2)`
D. `(3/2,2)`

Answer

C

Explanation

Given `y^(2)=2(x-3)`………….i
`implies2y(dy)/(dx)=2implies(dy)/(dx)=1/y`
Slope of the normal `=(-1)/((dy//dx))=-y`
Slope of the given line `=2`
`:.y=-2`
From eq. (i) when `y=-2`, then `x=5`
`:.` Required point is `(5,-2)`.