**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 ≡ x^{2} + y^{2} + 2gx + 2fy + c = 0 and S_{1} ≡ x^{2} + y^{2} + 2g_{1}x + 2fy + c_{1} = 0**.

Let *P*(*x*_{1}, *y*_{1}) be a point such that the lengths of tangents to the two circles are equal.

The locus of (*x*_{1}, *y*_{1}) is 2(*g* − *g*_{1})*x* + 2(*f* − *f*_{1})*y* + (*c* − *c*_{1}) = 0 which is a straight line.

Therefore, the radical ...

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