Let (x,y) be any point on the parabola `y^2 = 4x`. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Options

A. `x^(2)=y`
B. `x^(2)=2x`
C. `y^(2)=x`
D. `x^(2)=2y`

Answer

C

Explanation

`Let the corrdinate of P be (h,k).
`therefore h=(x+0)/(4),(y+0)/(4)`
`rArr x=4h,y=4k`
` on substituting in`y^(2) =4x,(4k)^(2)=4(4h)`
`rArr k^(2)=h` hence, y^(2) =x is requrired locus. `