Let O be the vertex and Q be any point on the parabola, x^2 = 8y

• 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.