Mathematics - Parabola Question with Solution | TestHub

Let $\mathrm{A}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ be any point outside the parabola and $\mathrm{B}(\alpha ,\beta ),\mathrm{C}\left({\alpha }^1,{\beta }^1\right)$ be the points of contact of tangents from point A eq of chord $\mathrm{BC},{\mathrm{YY}}_1=2\mathrm{a}\left(\mathrm{x}+{\mathrm{x}}_1\right)$ Lengths of ⟂ from A to BC $=\frac{2a\left(x_1+x\right)-y_{1}y}{\sqrt{y^2+4a^2}}=\frac{y_1^2-4ax}{\sqrt{y_1^2+4a^2}}$

Area of $\Delta \mathrm{ABC}=\frac{1}{2}\mathrm{AL}\times \mathrm{BC}$

We get $\frac{{\left({\mathrm{y}}_1^2-4{\mathrm{ax}}_1\right)}^{3/2}}{2a}$