= Common orthogonal line of two horocycles
= Common orthogonal lines of two horocycles
{synonym}
Two <horocycles> have a unique common orthogonal <hyperbolic line> when their <ideal centres of horocycles> differ: it is the line with those two <ideal endpoints>. If the centres agree, an <isometry> puts both <horocycles> on horizontal lines; every vertical <hyperbolic line> meets both orthogonally, so there are infinitely many. This classification remains valid for intersecting or tangent <horocycles>.
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