Recognising the equation of a circle.
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\nIf an equation is written in the form $cx^2+dx+ey^2+fy+g=0$, where $c,d,e,f,g$ are numbers, it could be a circle, but it might be something else (for example, an ellipse, a hyperbola, or even an empty graph). If the coefficients of $x^2$ and $y^2$ are the same (including the sign!) then the equation represents a circle. The coefficients being equal us to divide by that coefficient and start completing the square to get the equation into the standard form of a circle.
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", "$\\simplify[all]{x^2+(y-{ccy})^2={rs[1]}}$
", "$\\simplify[all]{(x-{ccx})^2={rs[2]}}$
", "$\\simplify[all]{{xmult}(x-{ccx})^2+{ymult}(y-{ccy})^2={rs[3]}}$
", "$\\simplify[all]{{ax}x^2+{bx}x+{ax}y^2+{by}y={rs[4]}}$
", "$\\simplify[all]{{ax}x^2+{bx}x+{ay}y^2+{by}y={rs[5]}}$
", "$\\simplify[all]{x^2+{bx}x-y^2+{by}y={rs[5]}}$
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