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:

Let P $(-a{t}_1^2,2a{t}_1),Q(-a{t}_1^2,-2a{t}_1)$  and R (h,k) By using section formula, we have $h=-a{t}_1^2,k=\frac{-2a{t}_1}{3},k=-\frac{2a{t}_1}{3}$

$\Rightarrow 3k=-2a{t}_1\Rightarrow 9k^2=4a^2{t_1}^2=4a(-h)\Rightarrow 9k^2=-4ah\Rightarrow 9k^2=-4h\Rightarrow 9y^2=-4x$