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AIEEE 2011

JEE Main 2011 Mathematics question on Conic Sections

Let (x,y)(x, y) be any point on the parabola y2=4xy^2 = 4x. Let PP be the point that divides the line segment from (0,0)(0, 0) to (x,y)(x, y) in the ratio 1:31:3. Then, the locus of PP is
  1. A.
    x2=yx^2 = y
  2. B.
    y2=2xy^2 = 2x
  3. C.
    y2=xy^2 = x
  4. D.
    x2=2yx^2 = 2y
Show answer and solution

Correct option: C

Solution

If P divides (0,0) to (x,y) in ratio 1:3, then P = (x/4, y/4). Let P = (h, k), so x = 4h, y = 4k. Since (x,y) lies on y² = 4x, substituting gives (4k)² = 4(4h), i.e., 16k² = 16h, so k² = h. The locus is y² = x.

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