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2026-04-01 17:22:38.1775064158
How to solve this hyperbolic problem?
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HINT.
Use the asymptotes as (oblique) coordinate axes. The equation of the hyperbola is then $xy=c^2$, where $c^2=(a^2+b^2)/2=61/2$. It is then easy to prove that: $$ y_L=y_P+y_Q=2y_R, $$ that is (if $P$ and $Q$ are on the same branch): $$ LO=PM+QN=2RE, $$ where $O$ is the origin.