Mathematics

Problem

Find the limiting points of the circles

(x^2 + y^2 + 2gx + c) + \lambda (x^2 + y^2 + 2fy + d) = 0

and show that the square of the distance between them is

\frac{(c-d)^2 - 4f^2g^2 + 4cf^2 + 4dg^2}{f^2 + g^2}