Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16

Question

$\begin {array} {1 1} (A)\;x^2+y^2+6x+8y+15=0 & \quad (B)\;x^2+y^2-6x+8y+15=0 \\ (C)\;x^2+y^2-6x-8y-15=0 & \quad (D)\;x^2+y^2-6x-8y+15=0 \end {array}$