Matrices and Determinants: JEE Main 2026 Mathematics question

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