Mathematics - Parabola Question with Solution | TestHub

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

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