If the pair of straight lines \( A x^{2}+2 H x y+B y^{2}=0 \) be conjugate diameters of the hype...

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If the pair of straight lines \( A x^{2}+2 H x y+B y^{2}=0 \) be conjugate diameters of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \), then prove that \( A a^{2}=B b^{2} \).
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