If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16 x+12 y+\mathrm{C}=0$, then $\mathrm{C}=$

If the shortest distance between the lines $\bar{r}_1=\alpha \hat{i}+2 \hat{j}+2 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k}), \lambda \in \mathbb{R}, \alpha>0 \quad$ and $\bar{r}_2=-4 \hat{i}-\hat{k}+\mu(3 \hat{i}-2 \hat{j}-2 \hat{k}), \mu \in R$, is 9 , then the value of $\alpha$ is

If two curves $x^2-4 y^2=2$ and $8 x^2=40-\mathrm{m} y^2$ are orthogonal to each other then $\mathrm{m}=$