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.

Find the radius of the circle (xcosalpha+ysinalpha-a)^2+(xsinalpha-ycosalpha-b)^2=k^2,ifalpha varies, the locus of its centre is again a circle. Also, find its centre and radius.

If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a circle, when m is (a) 1/2 (b). 1 (c). 2 (d). 3

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

Prove that locus of z is a circle and find its centre and radius if (z-i)/(z-1) is purely imaginary.

Find the value of a if 2x^(2)+ay^(2)-2x+2y-1=0 represents a circle and also find its radius. (ii) Find the values of a,b if ax^(2)+bxy+3y^(2)-5x+2y-3=0 represents a circle. Also find the radius and centre of the circle. (iii) If x^(2)+y^(2)+2gx+2fy=0 represents a circle with centre (-4,-3) then find g,f and the radius of the circle. (iv) If the circle x^(2)+y^(2)+ax+by-12=0 has the centre at (2,3) then find a ,b and the raidus of the circle. (v) If the circle x^(2)+y^(2)-5x+6y-a=0 has radius 4 , find a

Find the equation of the circle with: centre (-2,3) and radius 4.

Two points P and Q in the argand plane represent the complex numbers z and 3z+2+u . If |z|=2 , then Q moves on the circle, whose centre and radius are (here, i^(2)=-1 )

The equation I m((i z-2)/(z-i))+1=0, z & epsi; C , z!=i represents a part of a circle having radius equal to

Find the equation of the circle when the end points of a diameter are (5, -3) and (2, -4) . Also find its centre and radius.