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

$\begin{array}{1 1} \bigg(\frac{-6}{17},\frac{10}{17}\bigg) \\ \bigg(\frac{-8}{17},\frac{2}{17}\bigg) \\ \bigg(\frac{-4}{17},\frac{1}{17}\bigg) \\ \bigg(\frac{-7}{17},\frac{6}{17}\bigg) \end{array} $