what is co-axial circle how to determine its equation and also tell its figure

A system of circles, every pair of which has the same radical axis is called a coaxial system of circle. The radical axis of two circle is the locus of a point which moves in such a way that the length of the tangents drawn from it to the circles are equal.

The equation of a system of coaxial circle which the equation of the radical axis and one of the circle of the system are given.

S = x2 + y2 + 2gx + 2fy + c = o be the circle and L = lx + my + n = 0 be the radical axis, then

S + λ L = 0, λ is arbitrary constant, represents the coaxial system of circle. 


The equation of any two circle of the system are given.

S1 = x2 + y2 + 2g1 x + 2f1y + c1 = 0 and S2 = x2 + y2 + 2g2x + 2f2y + c2 = 0 be two circles of the system, then

S1+λ S2 = 0 (λ = – 1) represent the coaxial system of circle.


x2 + y2 + 2gx + c = 0, where g is a variable and c is constant is the simple form of the equation of coaxial system of circle. The common radical axis of the system is y-axis.

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