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JEE Advanced2011MathematicsParabolaActual

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 1: 3 . Then, the locus of P is

Options

  1. Ax^2=y
  2. By^2=2 x
  3. Cy^2=x
  4. Dx^2=2 y

Correct answer

C. y^2=x

Step-by-step solution

By section formula, h= x+0 4 , k= y+0 4 x=4 h and y=4 k Substituting in y^2=4 x , (4 k)^2=4(4 h) k^2=h or y^2=x is required locus.

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