Let the equation of the circle is, x2+y2+2gx+2gy+c=0 have center (−g,−f) . As it passes through the point (3, 4) So, 9+16+6g+8f=0 The circle is intersecting another circle (x2+y2=36) orthogonally, 2g(0)+f(0)−c−26 c=36 From above calculations, −6g−8f=61 By taking locus of the point (−g,−f) , we get 6x+8y−61=0