If $(x_1,y_1)$ and $(x_2,y_2)$ are ends of focal chord of  $y^2=4ax$ then $x_1{x}_2+y_1{y}_2=$

Take $(x_1,y_1)=(a{t}_1^2,2a{t}_1);(x_2,y_2)=(a{t}_2^2,2a{t}_2)$

Since focal chord $t_1{t}_2=-1$

Consider $x_1{x}_2+y_1{y}_2=a^2{t}_1^2{t}_2^2+4a^2{t}_1{t}_2$

$=a^2{\left(t_1{t}_2\right)}^2+4a^2{t}_1{t}_2$

$=a^2{(-1)}^2+4a^2(-1)$

$$\begin{gathered} =a^2-4a^2 \\ =-3a^2 \end{gathered}$$