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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` is `a^2(y^2-x^2)=4x^2y^2dot`

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To 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 given by \( a^2(y^2 - x^2) = 4x^2y^2 \), we can follow these steps: ### Step 1: Understand the Hyperbola and Normal Chords The equation of the hyperbola is given by: \[ x^2 - y^2 = a^2 \] A normal chord at a point \( (x_1, y_1) \) on the hyperbola will have its endpoints on the hyperbola. ...
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