If one end of a diameter of a circle x^2 + y^2 -4x-6y+11 =0 is (8, 4) show that coordinate of the other end are (-4, 2).
 

x²+y²-4x-6y+11=0
-4=2g
g=-2
-6=2f
f=-3
center=(-g,-f)
center=(2,3)
let the coordinate of other end of the diameter is x and y then,
2=x+8/2
x=-4
3=y+4/2
y=2
hence proved*