Question: Find the center and radius of common circle of the two spheres $x^2+y^2+z^2-x+z-2=0\,$ and $\,3(x^2+y^2)-8x-10y+8z+14=0$.
It is observed that the two spheres are orthogonal. But I am not able to find their common circle. It may be easy but I am not getting any idea. Can some one please throw a hint?