If a point P denoting the complex number z moves in the argand plane satisfying Re ( z-3 z+i )= 2 5 , then locus traced by z is x^2+y^2+a x+b y+c=0 . Find the value of (b-c-a) .

Step-by-step solution

Put z=x+i y , we get Re ( z-3 z+i )= 2 5 x(x-3)+y(y+1) x^2+(y+1)^2 = 2 5 5 (x^2+y^2-3 x+y )=2 (x^2+y^2+2 y+1 ) 3 x^2+3 y^2-15 x+y-2=0 or x^2+y^2-5 x+ 1 3 y- 2 3 =0 Hence on comparing, we get a=-5, b= 1 3 , c= -2 3 (b-c-a)=6