If the distance of the point $ P(43, \alpha, \beta) $ from the line $ \vec{r} = 4\hat{i} - \hat{k} + \mu(2\hat{i} + 3\hat{k}),; \mu \in \mathbb{R} $ along a line with direction ratios $ 3, -1, 0 $ is $ 13\sqrt{10} $, then $ \alpha^2 + \beta^2 $ is equal to ______