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 :

Explanation

Let `P(h,k)` is dividing the line segment from `(0,0)` and `(x,y)` in ratio `1:3`.

Then,

`h = (x+3(0))/(1+3) = x/4=> x = 4h`

`k = (y+3(0))/(1+3) = y/4 => y = 4k`

As `(x,y)` is a point on parabola `y^2 = 4x`,

so values of `x` and `y` will satisfy the equation.

`:. (4k)^2 = 4(4h)`

`=> 16k^2 = 16h`

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