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 $$f_3 < 0.$$ 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 the value of $$\left(\frac{1}{m_1^2} + m_2^2\right)$$ is