The locus of a point which divides the line segment joining the point (0, – 1) and a point on the parabola, x2 = 4y, internally in the ratio 1 : 2, is :

Engineering

Mathematics

Standard Parabola

Question

The locus of a point which divides the line segment joining the point (0, – 1) and a point on the parabola, x² = 4y, internally in the ratio 1 : 2, is :

9x² – 3y = 2

9x² – 12y = 8

4x² – 3y = 2

x² – 3y = 2

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Let point P be (2t, t²) and Q be (h, k).

$h = \frac{2 t}{3}, k = \frac{- 2 + t^{2}}{3}$

Hence locus is $3 k + 2 = {(\frac{3 h}{2})}^{2} \Rightarrow 9 x^{2} = 12 y + 8$