Find the equation of the circle which passes through the points $(2,3)$ and $(4,5)$ and the centre lies on the straight line $y-4x+3=0$.

Question

$\begin{array}{1 1}x^2+y^2+4x-10y+25=0\\x^2+y^2-4x-10y-38=0\\x^2+y^2-4x-10y+38=0\\x^2+y^2+4x+10y+25=0\end{array}$