Coordinate Geometry

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 = y
  2. y2 = x
  3. x2 = 2y
  4. y2 = 2x

Answer

P = (4t/4, 2t2/4)

h = t

k = t2/2

k = h2/2

⇨ 2y = x2

 

The correct option is C.