If the chords of contact of tangents from two poinst $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are at right angles, then find the value of $\frac{x_1{x}_2}{y_1{y}_2}\dot{}$

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