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(C) The equations of the chords of contact from points $(x_1, y_1)$ and $(x_2, y_2)$ to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are given

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$-\frac{a^4}{b^4}$

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(C) The equations of the chords of contact from points $(x_1, y_1)$ and $(x_2, y_2)$ to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are given by:$\frac{x x_1}{a^2} + \frac{y y_1}{b^2} = 1 \dots (i)$$\frac{x x_2}{a^2} + \frac{y y_2}{b^2} = 1 \dots (ii)$Since the chords are at right angles,the product of their slopes is $-1$.The slope of line $(i)$ is $m_1 = -\frac{b^2 x_1}{a^2 y_1}$.The slope of line $(ii)$ is $m_2 = -\frac{b^2 x_2}{a^2 y_2}$.Given $m_1 	imes m_2 = -1$,we have:$(-\frac{b^2 x_1}{a^2 y_1}) 	imes (-\frac{b^2 x_2}{a^2 y_2}) = -1$$\frac{b^4 x_1 x_2}{a^4 y_1 y_2} = -1$$\frac{x_1 x_2}{y_1 y_2} = -\frac{a^4}{b^4}$

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

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