= Parabola
{wiki}
A parabola is a <plane curve> whose points are equally distant from a focus and a directrix. In suitable coordinates it has equation $y=ax^2$, with $a\ne0$. Its quadratic geometry can also describe a <contour deformation> through a <saddle point>.
For example, take a <focus of a conic> at $(1,0)$ and a <directrix of a conic> $x=-1$. Equality of squared <Euclidean distances> gives $(x-1)^2+y^2=(x+1)^2$, hence $y^2=4x$. The point $(1,2)$ has distance $2$ to both the focus and the directrix. Its <eccentricity of a conic> is one. Unlike an <ellipse>, a <parabola> is unbounded and has only one matched focus-directrix description.
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