For the general second-degree expression
x2+y2+2gx+2fy+c=0,
answer the following without carrying out any numerical substitution.
(i) Write the coordinates of the centre of the curve represented by the above equation.
(ii) Give a clear justification for the statement: the expression represents a circle only when g2+f2−c>0. What happens when g2+f2−c≤0? Explain briefly.