The locus of a point which divides the line segment joining the point

Question:

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

  1. $9 x^{2}-3 y=2$

  2. $9 x^{2}-12 y=8$

  3. $x^{2}-3 y=2$

  4. $4 x^{2}-3 y=2$

Correct Option: , 2

Solution:

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