Let O be the vertex and Q be any point on the parabola, x 2 = 8 y . If the point P divides the line segment…

Let O be the vertex and Q be any point on the parabola, x2=8y. If the point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is
  1. x2=2y
  2. x2=y
  3. y2=x
  4. y2=2x

Solution

General point on x2=8y is Q4t,2t2

Let Ph,k divide OQ in ratio 1:3

h,k=14t+301+3,12t2+301+3

h,k=t,2t24

h=t & k=t22

k=h22

⇒  x2=2y  is the required locus. 

Asked in: JEE Main 2015 (04 Apr)

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