If the normal at the points $t_1$ and $t_2$ on $y^2=4ax$ intersect at the point $t_3$ on the parabola, then $t_1{t}_2=$

$\text{Normal at}{\mathrm{t}}_1\text{is}\mathrm{y}+{\mathrm{xt}}_1=2{\mathrm{at}}_1+{\mathrm{at}}_1^3\to \left(1\right)$

Equation of chord joining  $t_1\&t_3$ is $y(t_1+t_3)=2x+2a{t}_1{t}_3\to \left(2\right)$ 

(1) & (2) represents same

$\frac{t_1+t_3}{1}=\frac{-2}{t_1}\Rightarrow t_3=-t_1-\frac{2}{t_1}$

Similarly $t_3=-t_2-\frac{2}{t_2}$