\( \mathrm{B} \) and \( \mathrm{C} \) are fixed points having co-ordinates \( (3,0) \) and \( (-...

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\( \mathrm{B} \) and \( \mathrm{C} \) are fixed points having co-ordinates \( (3,0) \) and \( (-3,0) \) respectively. If the vertical angle \( \mathrm{BAC} \)
P is \( 90^{\circ} \), then the locus of the centroid of the \( \triangle \mathrm{ABC} \) has the equation :
(A) \( x^{2}+y^{2}=1 \)
(B) \( x^{2}+y^{2}=2 \)
(C) \( 9\left(x^{2}+y^{2}\right)=1 \)
(D) \( 9\left(x^{2}+y^{2}\right)=4 \)
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