Equation of common tangent to x² + y² = 2a² and y² = 8ax is

Equation of parabola y² = 8ax and x² + y² = 2a² be circle

 Eqn of tgt to parabola is $\mathrm{y}=\mathrm{mx}+\frac{2\mathrm{a}}{\mathrm{m}}$ 

it is also tangent to circle then d=r
$\Rightarrow \frac{\left|2\mathrm{a}\right|}{\sqrt{{\mathrm{m}}^4+{\mathrm{m}}^2}}\equiv \sqrt{2\mathrm{a}}\Rightarrow {\mathrm{m}}^2=-2 and m^2=1\Rightarrow \mathrm{m}=\pm 1$
sub m in (1) $\Rightarrow \mathrm{y}=\pm (\mathrm{x}+2\mathrm{a})$