Points $P$,$Q$ and $S$ are given. Construct the foci of hyperbola $H$ such that $P$ and $Q$ are its vertices and $S$ is one of its points.
How to solve this problem using only euclidean geometry methods?
2026-03-27 15:36:18.1774625778
Given two vertices and one point of hyperbola, construct its foci
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Construct through the midpoint $C$ of $PQ$ its perpendicular bisector, intersecting lines $SP$ and $SQ$ at $P'$ and $Q'$ respectively. Semi-conjugate axis $BC$ is the mean proportional between $CP'$ and $CQ'$.