Show that the orthogonal trajectories of the family of similar ellipses \( \frac{x^{2}}{a^{2}}+\...

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Show that the orthogonal trajectories of the family of similar ellipses \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=m^{2} \) for different values of \( m \) is \( x^{a^{2}}=A y^{b^{2}} \).
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