Let PQ be a double ordinate of the parabola y | vedclass

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(D) The equation of the parabola is $y^2 = -4x$,which is of the form $y^2 = -4ax$ with $a = 1$.Let the coordinates of $P$ be $(-t^2, 2t)$ and $Q$ be $

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$9y^2 = -4x$

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(D) The equation of the parabola is $y^2 = -4x$,which is of the form $y^2 = -4ax$ with $a = 1$.Let the coordinates of $P$ be $(-t^2, 2t)$ and $Q$ be $(-t^2, -2t)$,where $t > 0$ (since $P$ is in the second quadrant).Let $R(h, k)$ be the point that divides $PQ$ in the ratio $2 : 1$.Using the section formula,the coordinates of $R$ are:$h = \frac{2(-t^2) + 1(-t^2)}{2 + 1} = -t^2$$k = \frac{2(-2t) + 1(2t)}{2 + 1} = \frac{-4t + 2t}{3} = -\frac{2t}{3}$From $k = -\frac{2t}{3}$,we get $t = -\frac{3k}{2}$.Substituting $t$ into the equation for $h$:$h = -(-\frac{3k}{2})^2 = -\frac{9k^2}{4}$$4h = -9k^2$$9k^2 = -4h$Replacing $(h, k)$ with $(x, y)$,the locus of $R$ is $9y^2 = -4x$.

Let $PQ$ be a double ordinate of the parabola $y^2 = -4x$,where $P$ lies in the second quadrant. If $R$ divides $PQ$ in the ratio $2 : 1$,then the locus of $R$ is:

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