Mathematics - Parabola Question with Solution | TestHub

Suppose that the foci of the ellipse$\frac{x^2}{9}+ \frac{y^2}{5}=1$are$\left(f_1, 0\right) and (f_2, 0)$where$f_1>0 and f_2<0.$Let$P_1 and P_2$be two parabolas with a common vertex at (0, 0) and with foci at$\left(f_1, 0\right)$and$\left(2f_2, 0\right),$respectively. Let$T_1$be a tangent to$P_1$which passes through$\left(2f_2, 0\right)$and$T_2$be a tangent to$P_2$which passes through$(f_1, 0)$. If$m_1$is the slope of$T_1$and$m_2$is the slope of$T_2,$then the value of$\left(\frac{1}{m_1^2}+ m_2^2\right)$is