An ellipse whose major axis is parallel to x-axis is such that the segments of a focal chord are 1 and 3 units. The lines $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$ 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 ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{\alpha x}+2\mathrm{\beta y}-2\mathrm{\alpha }-1=0$. Then