The point \( \mathrm{P} \) moves in the plane of a regular hexagon such that the sum of the squa...

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The point \( \mathrm{P} \) moves in the plane of a regular hexagon such that the sum of the squares of its distances from the vertices of the hexagon is \( 6 \mathrm{a}^{2} \). If the radius of the circumcircles of the hexagon is \( r(a) \) then the locus of \( P \) is
(a) a pair of straight lines
(b) an ellipse
(c) a circle of radius \( \sqrt{\mathrm{a}^{2}-\mathrm{r}^{2}} \)
(d) an ellipse of major axis a and minor axis \( r \)
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