From any point on the hyperbola frac{x^2}{a^2 | vedclass

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(C) Let the point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $(x_0, y_0)$.The equation of the chord of contact of tangents drawn from

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$2ab$

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(C) Let the point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $(x_0, y_0)$.The equation of the chord of contact of tangents drawn from $(x_0, y_0)$ to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 2$ is given by $\frac{x x_0}{a^2} - \frac{y y_0}{b^2} = 2$.The asymptotes of the hyperbola are $\frac{x}{a} - \frac{y}{b} = 0$ and $\frac{x}{a} + \frac{y}{b} = 0$.It is a known property that for any point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = k$,the area of the triangle formed by the chord of contact and the asymptotes is constant and equal to $a b k$.Here,$k = 2$,so the area is $a b (2) = 2ab$.

From any point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,tangents are drawn to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 2$. The area of the figure formed by the chord of contact of that point and the asymptotes is

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