The circle x2+y2+2a1x+c=0lies completely inside the circle x2+y2+2a2x+c=0.Then,

The equation of radical axis of the given circle is x = 0. If one circle lies completely inside the other, the centers of both circles should lie on the same side of the radicalaxis and the radical axis should not intersect the circles. Therefore,−a1−a2>0 or a1a2>0Also, y2+c=0should have imaginary roots, i.e., c>0.