The locus of the centroid of the triangle formed by \( \mathrm{P}^{...

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The locus of the centroid of the triangle formed by
\( \mathrm{P}^{19: 5} \) any point \( P \) on the hyperbola

W \( 16 x^{2}-9 y^{2}+32 x+36 y-164=0 \), and its foci is
(1) \( 16 x^{2}-9 y^{2}+32 x+36 y-36=0 \)
(2) \( 9 x^{2}-16 y^{2}+36 x+32 y-144=0 \)
(3) \( 16 x^{2}-9 y^{2}+32 x+36 y-144=0 \)
(4) \( 9 x^{2}-16 y^{2}+36 x+32 y-36=0 \)
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