Length of the common chord of the parabola $y^2=$

$8x$and the circle $x^2+y^2-2x-4y=0$ is 

Any point on the parabola is $\left(2t^2,4t\right)$ which lies on
the circle if $t^4+3t^2-4t=0\Rightarrow t=0,1$

$\Rightarrow$end points of the common chord are (0, 0) and
(2, 4) and the required length is $2\sqrt{5}$.