If the chords of contact of tangents from two points \( \left(x_{1} y_{1}\right) \) and \( \left...

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If the chords of contact of tangents from two points \( \left(x_{1} y_{1}\right) \) and \( \left(x_{2}, y_{2}\right) \) to the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) are at right angles, then \( \frac{x_{1} x_{2}}{y_{1} y_{2}} \) is equal to
\( (A)-\frac{a^{2}}{b^{2}} \)
(B) \( -\frac{b^{2}}{a^{2}} \)
\( (C)-\frac{b^{4}}{a^{4}} \)
(D) \( -\frac{a^{4}}{b^{4}} \)
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