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Let (x,y) be any point on the parabola y...

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 :

A

`x^(2)=y`

B

`y^(2)=2x`

C

`y^(2)=x`

D

`x^(2)=2y`

Text Solution

Verified by Experts

The correct Answer is:
C
3
Point P(h,k) divides the line segment OR in ratio `1:3`. So, coordinates of point R are (4h,4k).
(Using ratio OP : PR = `1:3` )
Point R lies on the parabola
`:." "(4k)^(2)=4xx4hork^(2)=h`
Hence, locus is `y^(2)=x`.
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