Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola $x^{2} - y^{2} = a^{2}$ is $a^{2} (y^{2} - x^{2}) = 4 x^{2} y^{2} ˙$

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Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola

x^{2} - y^{2} = a^{2}

a^{2} (y^{2} - x^{2}) = 4 x^{2} y^{2} ˙

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Question Text

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola

x^{2} - y^{2} = a^{2}

a^{2} (y^{2} - x^{2}) = 4 x^{2} y^{2} ˙

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