Eigenvalues and Circle Axis Intersections

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