Mathematics - Parabola Question with Solution | TestHub

$\mathrm{ar}△ABC=\frac{1}{2}\left|\begin{array}{ccc}a{t}_1^2& a{t}_2^2& a{t}_3^2\\ 2a{t}_1& 2a{t}_2& 2a{t}_3\\ 1& 1& 1\end{array}\right|=a^2\left|\left(t_2-t_1\right)\left(t_3-t_2\right)\left(t_1-t_3\right)\right|$ Also $△PQR=\frac{1}{2}\left|\begin{array}{ccc}a{t}_1{t}_2& a{t}_2{t}_3& a{t}_3{t}_1\\ a\left(t_1+t_2\right)& a\left(t_2+t_3\right)& a\left(t_3+t_1\right)\\ 1& 1& 1\end{array}\right|=\frac{a^2}{2}\left|\left(t_3-t_1\right)\left(t_1-t_2\right)\left(t_2-t_3\right)\right|$$\Rightarrow \frac{\mathrm{ar}△ABC}{\mathrm{ar}△PQR}=2$