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An ellipse and hyperbola share common fo...

An ellipse and hyperbola share common foci F1, and F2. The ellipse has vertices at the origin and (0, 24) and a semi-minor axis of length 11. The hyperbola has a conjugate axis of length `4sqrt(3)` . The ellipse and hyperbola intersect at four points. Let P be one of the points of intersection, then value of `(P F_1)^2+(P F_2)^2` is.
(a) 410
(b) 820
(c) 532
(d) 266

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