Question

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

• A. $9x^2 - 12y = 8$
• B. $4x^2 - 3y = 2$
• C. $x^2 - 3y = 2$
• D. $9x^2 -3y = 2$

Answer 1

Answer: (A)

$9x^2 - 12y = 8$

Answer 2

$\Rightarrow 3h = 2t$ and $3k = t^{2} - 2$
$\Rightarrow 3y=\left(\frac{3x}{2}\right)^{2}-2 \Rightarrow 12y=9x^{2}-8$