Equation of a Circle Assignment Help

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Equation of a Circle:

Suppose  a   fixed  complex  number z0 and take z  be  any   complex  number  which  moves  in  such a path that it's distance from  z0  is always  same to 'r'. That implies z could lie on a  circle  whose   centre  is  z0  and  radius  r. And it's equation could be |z -z0| = r .

946_Equation of a Circle.png       

2323_Equation of a Circle1.png, where centre = -a and radius = 310_Equation of a Circle2.png

Example : If z1, z2, z3 are complex numbers such that 155_Equation of a Circle5.png,  denotes that the points shown by z1, z2, z3 lie on a circle passing through the origin.

Solution:        Since P(z1), Q(z2), R(z3) and S(z4) are concyclic points,

                 1244_Equation of a Circle3.png

          931_Equation of a Circle4.png

                        =>1/2 = real, which is true.

                                    Hence z1, z2, z3 and the origin are concyclic.

 

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