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 :
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t2 = 4h, y=2k
so 4k2 = 4h
k2 = h
Hence required locus is y2 = x
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