Find the equation to the circle which passes through the origin and has its center on the line x + y + 4 = 0 and cuts the circle x2+y2−4x+2y+4=0 orthogonally.
Find the equation of circle which touches 2x − y + 3 = 0 and pass through the points of intersection of the line x + 2y − 1 = 0 and the circle x2 + y2 − 2x + 1 = 0