= Implicit equation
{title2=$F(x,y)=0$}
An <implicit equation> specifies a relation between variables without isolating a designated output as an explicit <function> of the inputs. For example, $x^2+y^2=1$ specifies a <circle>. On $-1<x<1$, it determines the two real branches $y=\pm\sqrt{1-x^2}$, each an <implicit function> when one branch is selected. The <implicit function theorem> gives local conditions for a unique differentiable branch; <implicit differentiation> computes its <derivative> without first solving explicitly.
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