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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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detailed solution

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+t23 Hence 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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$The locus of a point which divides the line segment joining the point (0, - 1) and a point$ $on the parabola x^{2} = 4 y internally in the ratio 1 : 2 is:$