The equation of circle Re(z2)+2[Im(z)]2+2Re(z)=0, where z=x+iy cc⇒(x2−y2)+2y2+2x=0 ⇒[∵z2=(x2−y2)+2xyi] ⇒x2+y2+2x=0 (x+1)2+y2=1 Centre =(−1,0) Now, parabola ⇒x2−6x−y+13=0 ⇒x2−6x+9=y−4 ⇒(x−3)2=y−4 Vertex = Equation of line passing through centre( −1,0) and vertex (3,4) is y−0=
4−0
3+1
(x+1)⇒y=x+1 On comparing, y=mx+c ⇒y-intercept =1