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

- x
^{2}= y - y
^{2}= x - x
^{2}= 2y - y
^{2}= 2x

**Answer**

P = (4t/4, 2t^{2}/4)

h = t

k = t^{2}/2

k = h^{2}/2

⇨ 2y = x^{2}

**The correct option is C.**