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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
Let the coordinate of P be (h, k).
`:." "h=(x+0)/(4),k=(y+0)/(4)`
`impliesx=4h,y=4k`
Given equation of parabola be
`y^(2)=4x`
`:.(4k)^(2)=4(4h)`
`implies" "k^(2)=h`
Hence, locus of P is `y^(2)=x`
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