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  4. 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 :

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Q. 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 :

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Solution:

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

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