Let L_1, L_2 be the lines passing through the point P(0,1) and touching the parabola 9 x^2+12 x+18 y-14=0. Let Q and R be the points on the lines L_1…

Let $\displaystyle L_1, L_2$ be the lines passing through the point $\displaystyle P(0,1)$ and touching the parabola $\displaystyle 9 x^2+12 x+18 y-14=0$. Let $\displaystyle Q$ and $\displaystyle R$ be the points on the lines $\displaystyle L_1$ and $\displaystyle L_2$ such that the $\displaystyle \triangle P Q R$ is an isosceles triangle with base $\displaystyle Q R$. If the slopes of the lines $\displaystyle Q R$ are $\displaystyle m_1$ and $\displaystyle m_2$, then $\displaystyle 16\left(m_1^2+m_2^2\right)$ is equal to $\displaystyle \_\_\_\_$.