The equation of the circle which passes through the origin and cuts orthogonally each of the circles $x^2+y^2-6x+8=0$ and $x^2+y^2-2x-2y=7$ is :

Question

$$\begin {array} {1 1} (1)\;3x^2+3y^2-8x-13 y=0 & \quad (2)\;3x^2+3y^2-8x+29y=0 \\ (3)\;3x^2+3y^2+8x+29 y=0 & \quad (4)\;3x^2+3y^2-8x-29 y=0 \end {array}$$