Find the conditions under which the orthogonal trajectories of families of ellipses x 2 /a 2 +

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Find the conditions under which the orthogonal trajectories of families of ellipses x2/a2 + y2/b2 = c are again conic sections. Illustrate your result graphically by sketches or by using your CAS. What happens if a → 0? If b → 0?

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