%FP and FQ should coincide
\fill  (FP) circle(2pt);
\fill  (FQ) circle(2pt);

\draw [tangents] ($(P)!\ttangent!(FP)$) -- ($(FP)!\ttangent!(P)$);
\draw [tangents]($(FQ)!\ttangent!(Q)$) -- ($(Q)!\ttangent!(FQ)$);
