The normal at a point $\left({{{\mathrm{bt}}_1}^2}_{ },2{\mathrm{bt}}_1\right)$ on a parabola meets the parabola again at the point $\left({{\mathrm{bt}}_2}^2, 2{\mathrm{bt}}_2\right)$ then

Equation of normal at $\left(\mathrm{b} {{\mathrm{t}}_1}^2, 2{\mathrm{bt}}_1\right)$ for ${\mathrm{y}}^2=4\mathrm{ax}$ is ${\mathrm{t}}_1\mathrm{x}+\mathrm{y}=2{\mathrm{bt}}_1+{{\mathrm{bt}}_1}^3$ it is also passing through $\left(\mathrm{b} {{\mathrm{t}}_2}^2, 2{\mathrm{bt}}_2\right)$

$$\begin{gathered} {\mathrm{t}}_1\left({b{t}_2}^2\right)+2b{t}_2=2b{t}_1+b{t_1}^3 \\ b{t}_1{{\mathrm{t}}_2}^2+2b{t}_2=2b{t}_1+{b{t}_1}^3 \\ b{t}_1{{\mathrm{t}}_2}^2-{b{t}_1}^3=2b{t}_1-2b{t}_2 \\ b{\mathrm{t}}_1\left[{{\mathrm{t}}_2}^2-{{\mathrm{t}}_1}^2\right]=2b\left[{\mathrm{t}}_1-{\mathrm{t}}_2\right] \\ -{\mathrm{t}}_1\left[{\mathrm{t}}_1+{\mathrm{t}}_2\right]=2 \\ \Rightarrow t_2=-t_1-\frac{2}{t_1} \end{gathered}$$