Explanation:
The standard form of the equation of a circle is ...
(x -h)² +(y -k)² = r² . . . . . . circle centered at (h, k) with radius r
The general form of the equation of a circle will be ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0 . . . . . A = C for a circle
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The former is converted to the latter by eliminating parentheses, subtracting r² and collecting terms.
x² +y² -2hx -2ky +(h² +k² -r²) = 0
This shows you that ...
A = C = 1
B = 0
D = -2h
E = -2k
F = h² +k² -r²
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In general form, we like to have the coefficients be mutually prime integers and the leading coefficient be positive. That is not always possible, depending on the circle being represented.
