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.

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

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

Find the equation of the circle the end point of whose diameter are (2,-3) and (2,4). Find its centre and radius.

Find the equation of the circle, the end points of whose diameter are (2, -3) and (-2, 4) . Find its centre and radius.

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

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

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

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