If the equation $ax^{2}-6xy+y^{2} ; + 2gx+2fy+c=0$ represents a pair of line whose slopes are $m$ and $m^{2}$, then sum of all possible values of $a$ ; is-

Point $Q$ lies on the circle having diameter $O P$. The locus of point $Q$

$\begin{array}{l} (x-0)(x-h)+(y-0)(y-k)=0 \\ x^{2}+y^{2}-h x-k y=0 \\ \begin{array}{l} a x^{2}-6 x y+y^{2}+2 g x+2 f y+c=0 \\ a x^{2}=\left(y+m x+c_{1}\right)\left(y+m^{2} x+c_{2}\right) \end{array} \\ y^{2}+m^{2} x y+c_{2} y+m x y+m^{3} x^{2}+m x c_{2}+c_{1} y+c_{1} m^{2} x\\ a=m^{3} \\ m^{2}+m=-6 \Rightarrow m^{2}+m=0 \\ +\mathrm{C}_{2} \mathrm{C}_{2} \\ a=8,-27 \\ m^{2}+3 m-2 m-6=0 \\ m(m+3)-2(m+3)=0 \\ \text { total possible of m } \\ (m-2)(m+3)=0 \\ m=2,-3 \\ =-19 \\ \end{array}$