1. The problem is to state the general form of a circle's equation. 2. The standard form of a circle's equation with center $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. To write this in the general form, expand the squares: $$ (x - h)^2 + (y - k)^2 = r^2 \implies (x^2 - 2hx + h^2) + (y^2 - 2ky + k^2) = r^2 $$ 4. Combine like terms: $$ x^2 + y^2 - 2hx - 2ky + (h^2 + k^2 - r^2) = 0 $$ 5. Let $D = -2h$, $E = -2k$, and $F = h^2 + k^2 - r^2$, then the general form is: $$ x^2 + y^2 + Dx + Ey + F = 0 $$ 6. This is the general form of a circle's equation, where $D$, $E$, and $F$ are constants. This form is useful for identifying the circle's center and radius by completing the square if needed.