The equations of the sides AB, BC and CA of a triangle ABC are: 2 x+y=0, x+p y=21 a,(a ≠ 0) and x-y=3 respectively. Let P (2, a ) be the centroid of…

The equations of the sides $\displaystyle \mathrm{AB}, \mathrm{BC}$ and CA of a triangle ABC are : $\displaystyle 2 x+y=0, x+p y=21 a,(a \neq 0)$ and $\displaystyle x-y=3$ respectively. Let $\displaystyle \mathrm{P}(2, \mathrm{a})$ be the centroid of $\displaystyle \Delta \mathrm{ABC}$. Then $\displaystyle (\mathrm{BC})^2$ is equal to