A parabola is drawn to pass through \( \mathrm{A} \) and \( \mathrm...

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A parabola is drawn to pass through \( \mathrm{A} \) and \( \mathrm{B} \), the ends of a diameter of a given circle of radius \( \mathrm{a} \), and to have as directrix a tangent to a concentric circle of radius \( b \); then axes being \( A B \) and a perpendicular
\( \mathrm{P} \) diameter, prove that the locus of the focus of the parabola is \( \frac{x^{2}}{b^{2}}+\frac{y^{2}}{b^{2}-a^{2}}=1 \)

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