An ellipse whose major axis is parallel to x−axis is such that the segments of a focal chord are of 1 and 3 units. The lines ax+by+c=0 are the chords of the ellipse such that a,b,c are in A.P. and bisected by the point at which they are concurrent. The equation of auxiliary circle is
x2+y2+2αx+2βy−2α−1=0. Then