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

Vertex of the parabola x²=8y is O(0,0)
And any point on the parabola is Q(4t,2t²)
Let P(h,k) divides the line segment OQ internally in the ratio 1:3
⇒h=(3×0+1×4t)/(1+3) = t
and k=(3×0+1×2t²)/(1+3) = t²/2
Eliminating t we get, h²=2k
Hence the locus of p(h,k) is, x²=2y