№2080
\[\begin{array}{l}
{\text{Line }}AB{\text{ is normal line to lemniscate }}\rho {\text{ = }}\sqrt {\cos 2\varphi } {\text{ at point }}A{\text{ and is tangent to the lemniscate}} \hfill \\
{\text{at point }}B{\text{ (see pic}}{\text{.)}}{\text{. Find coordinates of points }}A{\text{ and }}B,{\text{ }}\left| {AB} \right|{\text{ and equation of line }}AB. \hfill \\
\end{array} \]
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smart: 10