Question: Show that the ellipse x2/a2 + y2/b2 = 1 and the hyperbola x2 / A2 - y2/B2 = 1 are orthogonal trajectories if A2 <

Show that the ellipse x2/a2 + y2/b2 = 1 and the hyperbola x2 / A2 - y2/B2 = 1 are orthogonal trajectories if A2 < a2 and a2 - b2 = A2 + B2 (so the ellipse and hyperbola have the same foci).

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