
Let

be the centroid of the triangle

Prove that all conics passing through the points

are hyperbolas.

Find the locus of the centers of these hyperbolas.
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$(BEL 5)$ Let $G$ be the centroid of the triangle $OAB.$
$(a)$ Prove that all conics passing through the points $O,A,B,G$ are hyperbolas.
$(b)$ Find the locus of the centers of these hyperbolas.