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 = *x*^{2} + *y*^{2} + 2*gx* + 2*fy *+ *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.

S_{1} = *x*^{2} + *y*^{2} + 2*g*_{1} *x* + 2*f*_{1}*y* + *c*_{1} = 0 and S_{2} = *x*^{2} + *y*^{2} + 2*g*_{2}*x* + 2*f*_{2}*y *+ *c*_{2} = 0 be two circles of the system, then

S_{1}+λ S_{2} = 0 (λ = – 1) represent the coaxial system of circle.

*x*^{2} + *y*^{2 }+ 2*gx* + *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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