A series of hyperbolas is drawn having a common \( \mathrm{P} \) tr...

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A series of hyperbolas is drawn having a common
\( \mathrm{P} \) transverse axis of length \( 2 a \). Prove that the locus of a point \( P \) on each hyperbola such that its distance from
W. the transverse axis is equal to its distance from on asymptote, is the curve
\[
\left(x^{2}-y^{2}\right)^{2}=4 x^{2}\left(x^{2}-a^{2}\right)
\]
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