Engineering
Mathematics
Standard Parabola
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 :

x2 = y

x2 = 2y

y2 = 2x

y2 = x

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Solution

 h=t24,k=2t4     

t2 = 4h, y=2k

so 4k2 = 4h

  k2 = h

Hence required locus is y2 = x

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