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

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