If the power of origin w.r.t the circle on a focal chord of ${\mathrm{y}}^2=4\mathrm{ax}$ as a dia meter is _______

Equation of the circle having focal chord of parabola $y^2=4ax as diametre is$

$\left(\mathrm{x}-{\mathrm{at}}^2\right) \left(\mathrm{x}-\frac{\mathrm{a}}{{\mathrm{t}}^2}\right)+\left(y-2\mathrm{at}\right) \left(\mathrm{y}+\frac{2\mathrm{a}}{\mathrm{t}}\right)=0$

Power of origin $={\mathrm{S}}_{11}={\mathrm{a}}^2-4{\mathrm{a}}^2=-3{\mathrm{a}}^2$