Question

Condition that a general.equation of second degree in x,y may be represent a circle

Answer 1

This is the general equation of a circle
${x}^{2} + {y}^{2} + 2gx + 2fy + h = 0$
So I think following could be the conditions
1. Coefficients of x square and y square are equal and non zeros
2. There are no non-linear terms
3. g and f are constants and not functions of x and y