The area of the triangle formed by the tangent to the curve $x y=\mathrm{a}^2$ at $\left(x_1, y_1\right)$ on it and the axes is

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Aicharya · Accepted Answer

let Point $P$ be $\left(a t, \frac{a}{t}\right)$

$\begin{aligned} & \because x y=a^2 \\ & \text { eqn of tangent at } P \text { : }\end{aligned}$ $t y+\frac{x}{t}-2 a=0$ When $y=0$ : $x = 2 a t$ $A(2 a t, 0)$ When $x=0$ $y=\frac{2 a}{t}$ $\therefore B\left(0, \frac{2 a}{t}\right)$. $\therefore \triangle A B O$ if a right $\angle \triangle$ $\therefore \operatorname{ar}(\triangle A B O)=\frac{1}{2} \times \frac{2 a}{t} \times 2 a t=2 a^2$

The area of the triangle formed by the tangent to the curve $x y=\mathrm{a}^2$ at $\left(x_1, y_1\right)$ on…

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