If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$ (for some fixed $k$) at a point $(\alpha, \beta)$; then $(\alpha, \beta)$ is:

Question

( A ) $(-\frac{6}{17}, \frac{10}{17})$
( B ) $(-\frac{7}{17}, \frac{6}{17})$
( C ) $(-\frac{8}{17}, \frac{2}{17})$
( D ) $(-\frac{4}{17}, \frac{1}{17})$