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(C) The given parabola is $y^2=12x$. Comparing with $y^2=4ax$,we get $a=3$. The focus is $(3, 0)$.Let $Q(3t^2, 6t)$ be a point on the parabola.Point $

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$y^2=4(x-2)$

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(C) The given parabola is $y^2=12x$. Comparing with $y^2=4ax$,we get $a=3$. The focus is $(3, 0)$.Let $Q(3t^2, 6t)$ be a point on the parabola.Point $P(x, y)$ divides the segment joining $(3, 0)$ and $(3t^2, 6t)$ in the ratio $1:2$.Using the section formula,$P(x, y) = \left(\frac{1(3t^2) + 2(3)}{1+2}, \frac{1(6t) + 2(0)}{1+2}\right) = \left(\frac{3t^2+6}{3}, \frac{6t}{3}\right) = (t^2+2, 2t)$.Thus,$x = t^2+2$ and $y = 2t$.From $y = 2t$,we get $t = \frac{y}{2}$.Substituting $t$ into the equation for $x$: $x = (\frac{y}{2})^2 + 2 = \frac{y^2}{4} + 2$.$x - 2 = \frac{y^2}{4} \Rightarrow y^2 = 4(x-2)$.

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12x$ and a point on the parabola in the ratio $1:2$,then the locus of $P$ is:

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