If the parabola $y^2=4b\left(x-c\right)$ and $y^2=8ax$ have a common normal other than X-axis then which one of the following is a best choice for the ordered triad $\left(a,b,c\right)$

Equation of normal to$y^2=4b\left(x-c\right)$ is  $y=m(x-c)-2bm-b{m}^3$ and

Equation of normal to $y^2=8ax$  is
$y=mx-4am-2a{m}^3(m\ne 0)$ 

for common normal

$$\begin{gathered} -cm-2bm-b{m}^3=-4am-2a{m}^3 \\ {m}^3(2a-b)=m(2b-4a+c) \\ m=0 or m^2=\frac{c}{2a-b}-2>0 \end{gathered}$$

$\frac{c}{2a-b}>2$, check the options