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

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4x2−3y=2

x2−3y=2

9x2−3y=2

9x2−12y=8

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Correct option is D

Let P(0, -1) , Q2t,t2 and R (h, k) Given that R divides PQ in 1:2,∴h=2t3,k=−2+t23Hence locus is 3k+2=3h22⇒9x2=12y+8

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