ParabolaHard

Question

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 1 : 3. Then the locus of P is

Options

A.x2 = y
B.y2 = 2x
C.y2 = x
D.y2 = 2y

Solution

         y2 = 4x
and Q will lie on it
⇒ (4k)2 = 4 × 4h
⇒ k2 = h
⇒ y2 = x (replacing h by x and k by y)

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