Are you smarter than me?

Geometry Level 4

\(Tangent\quad drawn\quad to\quad ellipse\quad { x }^{ 2 }+{ 2y }^{ 2 }=6\quad at\quad point\quad (2,1).If\quad A\\ and\quad B\quad are\quad the\quad feet\quad of\quad pependiculars\quad from\quad the\quad two\\ focii\quad on\quad the\quad tangent,then\quad length\quad AB\quad equals\quad \)

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