Q.

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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a

x2=y

b

5y2=2x

c

5y2=8x

d

5x2=2y

answer is C.

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Detailed Solution

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