Question

Equation of circle passing through intersection of two circles and touches a line

Answer 1

Clearly, it represents a circle for all values of λ except λ = -1. For λ = -1 (iii) becomes a first degree equation in x, y which represents a line. In order to prove that it passes through the points of intersection of the two given circles, it is sufficient to show that their points of intersection satisfy (iii).