Mathematics - Parabola Question with Solution | TestHub

${\mathrm{t}}_1{\mathrm{t}}_2=-1$

Clearly ABCD is a rectangle Co-ordinate of $B\left(t_1{t}_2,\left(t_1+t_2\right)\right)$

$$\begin{array}{c}AB=\left|\left(t_2-t_1\right)\right|\sqrt{1+t_1^2}BC=\left(t_2-t_1\right)\sqrt{1+t_2^2}\text{ Area }=AB\times BC={\left(t_2-t_1\right)}^2\sqrt{\left(1+t_1^2\right)\left(1+t_2^2\right)}={\left(t_1+\frac{1}{t_1}\right)}^3\end{array}$$

Least value $=8$.