Let A = [1, 2, 7; 4, -2, 8; 3, 8, -7] and det ( A -α I )=0, where α is a real number. If the largest possible value of α is p, then the circle…

Let $\displaystyle \mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 7 \\ 4 & -2 & 8 \\ 3 & 8 & -7\end{array}\right]$ and $\displaystyle \operatorname{det}(\mathrm{A}-\alpha \mathrm{I})=0$, where $\displaystyle \alpha$ is a real number. If the largest possible value of $\displaystyle \alpha$ is $\displaystyle p$, then the circle $\displaystyle (x-p)^2+(y-2 p)^2=320$, intersects the co-ordinate axes at