Suppose that the foci of the ellipse $$\frac{x^2}{9}+\frac{y^2}{5}=1$$ are $$(f_1,0)$$ 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 $$(f_1,0)$$ and $$(2f_2,0)$$ respectively. Let $$T_1$$ be a tangent to $$P_1$$ which passes through $$(2f_2,0)$$ 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 find the value of $\left( \frac{1}{m_1^2}+m_2^2 \right)$