If the distance of the point P (43, α, β), β<0, from the line r =4 i - k +μ(2 i +3 k ), μ ∈ R along a line with direction ratios 3, -1, 0 is 13 √ 10,…

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