Question

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 :

Answer 1

Correct Answer - C
By section formula,
`h = (x + 0)/(4), k = (y + 0)/(4)`
`:. X = 4 h, y = 4 k`

Substituting in `y^(2) = 4x`,
`(4 k)^(2) = 4 (4h)`
`implies k^(2) = h`
or `y^(2) = x` is required locus.