Equation of the circle which passes through the origin and cuts orthogonally each of the circles x2+y2−4x−6y−3=0  is:

Equation of the circle through origin is x2+y2+2gx+2fy=0                                              ……(1)It intersects the circlesx2+y2−8y+12=0  and x2+y2−4x−6y−3=0  orthogonally, so0−8f=12+0⇒f=−3/2 and    −4g−6f=−3+0⇒g=3 .Hence, the required circle isx2+y2+6x−3y=0 .