System of Circles
5.1 RADICAL AXIS OF TWO CIRCLES
Definition 5.1.1: The radical axis of two circles is defined as the locus of a point such that the lengths of tangents from it to the two circles are equal.
Obtain the equation of the radical axis of the two circles S ≡ x2 + y2 + 2gx + 2fy + c = 0 and S1 ≡ x2 + y2 + 2g1x + 2fy + c1 = 0.
Let P(x1, y1) be a point such that the lengths of tangents to the two circles are equal.
The locus of (x1, y1) is 2(g − g1)x + 2(f − f1)y + (c − c1) = 0 which is a straight line.
Therefore, the radical ...