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Analytical Geometry by P. R. Vittal

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Chapter 5

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 Sx2 + y2 + 2gx + 2fy + c = 0 and S1x2 + y2 + 2g1x + 2fy + c1 = 0.

equation

Let P(x1, y1) be a point such that the lengths of tangents to the two circles are equal.

equation

The locus of (x1, y1) is 2(gg1)x + 2(ff1)y + (cc1) = 0 which is a straight line.

Therefore, the radical ...

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