Find the area of the triangle formed with the coordinate axes and the tangent drawn at the point (x₁, y₁) on the circle x² + y² = a²

$\text{ Circle is }{\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2$
Equation of tangent at $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\text{ is }{\mathrm{S}}_1=0$
$\Rightarrow {\mathrm{xx}}_1+{\mathrm{yy}}_1-{\mathrm{a}}^2=0 ...\left(1\right)$

If this tangents forms $∆$OAB with coordinate axes,
$\text{ Then, Area of }\mathrm{△}\mathrm{OAB}=\frac{{\mathrm{C}}^2}{2\left|\mathrm{ab}\right|}$
$\text{ Here, }\mathrm{a}={\mathrm{x}}_1,\mathrm{b}={\mathrm{y}}_1,\mathrm{c}=-{\mathrm{a}}^2 ...\mathrm{eq}\left(1\right)$
$\therefore \text{ Area of }\mathrm{△}\mathrm{OAB}=\frac{{\left(-{\mathrm{a}}^2\right)}^2}{2\left|{\mathrm{x}}_1\cdot {\mathrm{y}}_1\right|}=\frac{{\mathrm{a}}^4}{2\left({\mathrm{x}}_1{\mathrm{y}}_1\right)}\text{ sq.units }$