If the coordinates of ends of a focal chord of the parabola y² = 4ax are (x₁,y₁) and (x₂,y₂). Then P.T ${\mathrm{x}}_1{\mathrm{x}}_2={\mathrm{a}}^2,{\mathrm{y}}_1{\mathrm{y}}_2=-4{\mathrm{a}}^2$

$\text{ Let }\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=\left({\mathrm{at}}_1^2,2{\mathrm{at}}_1\right)$
$\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)=\left({\mathrm{at}}_2^2,2{\mathrm{at}}_2\right)$ are end of focal chord then 

 we know that ${\mathrm{t}}_1{\mathrm{t}}_2=-1$
${\mathrm{x}}_1{\mathrm{x}}_2={\mathrm{a}}^2{\left({\mathrm{t}}_1{\mathrm{t}}_2\right)}^2={\mathrm{a}}^2(-1{)}^2={\mathrm{a}}^2$

${\mathrm{y}}_1{\mathrm{y}}_2=4{\mathrm{a}}^2\left({\mathrm{t}}_1{\mathrm{t}}_2\right)=4{\mathrm{a}}^2(-1)=-4{\mathrm{a}}^2$