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Suppose that the foci of the ellipse (x^...

Suppose that the foci of the ellipse `(x^(2))/(9)+(y^(2))/(5)=-1` are `(f_(1),0)` and `(f_(2),0)` where `f_(1)gt0` and `f_(2)lt0`. 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 `((1)/(m_(1)^(2))+m_(2)^(2))` is -

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