Show that `|(z -2)/(z - 3)| = 2` represents a circle, find its centre and radius.

If |(z-2)/(z-3)|=2 represents a circle, then find its radius.

Show that the equaion x ^(2) + y ^(2) - 6x + 4y - 36 = 0 represents a circle. Also, find its centre and radius.

Show that the equation x^(2)+y^(2)+x-y=0 represents a circle find its centre and radius.

Show that the equation 3x^(2)+3y^(2)+6x-4y-1=0 represents a circle Find its centre and radius.

Show that the equation 3x^(2)+3y^(2)+12x-18y-11=0 represent a circle.Also find its centre and radius.

If z=2 + t + i sqrt(3-t^2) , where t is real and t^2 lt 3 , show that the modulus of (z+1)/(z-1) is independent of t. Also show that the locus of the points z for different values of t is a circle and finds its centre and radius.

Show that the equation x ^(2) + y ^(2) + 2x + 10 y + 26 = 0 represents a point circle. Also, find its centre.

If Re ((z + 2i)/(z+4))= 0 then z lies on a circle with centre :