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Let $(x, y)$ be any point on the parabola $y^{2} = 4 x$ . Let P be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $2 : 3$ . Then locus of $P$ is

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x2=y

5y2=2x

5y2=8x

5x2=2y

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detailed solution

Correct option is C

Let P be (h, k)then h=2x5, k=2y5 As (x, y) lies on the parabola y2=4x 5k22=45h2⇒ 5k2=8h⇒Locus of P is 5y2=8x.

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Let (x, y) be any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0,0) to (x, y) in the ratio 2:3. Then locus of P is

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Ready to Test Your Skills?

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Let $(x, y)$ be any point on the parabola $y^{2} = 4 x$ . Let P be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $2 : 3$ . Then locus of $P$ is