= Polar equation of a conic
{title2=$r=\ell/(1+e\cos\theta)$}
A <conic section> with a <focus of a conic> at the origin has the <polar coordinates> <equation> $r=\ell/(1+e\cos\theta)$, where $\ell>0$ is the <semilatus rectum> and $e\geq0$ the <eccentricity>. The <directrix of a conic> definition $r=e(d-r\cos\theta)$ gives the formula with $\ell=ed$ when $e>0$; $e=0$ is the <circle> limit. The cases $0<e<1$, $e=1$, and $e>1$ give an <ellipse>, <parabola>, and <hyperbola>. The physical <radius> requires a positive <denominator>. For an attractive inverse-square <central force>, the <Laplace-Runge-Lenz vector> gives $\ell=mh^2/k$ and $e=A/(mk)$.
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