Mathematics - Parabola Question with Solution | TestHub

$\mathrm{A}(0,2),\mathrm{B}=\left({\mathrm{t}}_1^2-4,{\mathrm{t}}_1\right)\mathrm{C}=\left({\mathrm{t}}^2-4,\mathrm{t}\right)$ $\frac{2-t_1}{4-t_1^2}\cdot \frac{t_1-t}{t_1^2-t^2}=-1\Rightarrow \frac{1}{2+t_1}\cdot \frac{1}{t+t_1}=-1\Rightarrow t_1^2+(2+t)t_1+(2t+1)=0$

For real ${\mathrm{t}}_1,\Rightarrow (2+\mathrm{t}{)}^2-4(2\mathrm{t}+1)=0\Rightarrow {\mathrm{t}}^2-4\mathrm{t}\ge 0\Rightarrow \mathrm{t}\in (-\alpha ,0]\cup [4,\alpha )$