Let the lines y+2 x=√ 11 +7 √ 7 and 2 y+x=2 √ 11 +6 √ 7 be normal to a circle C:(x-h)^2+(y-k)^2=r^2. If the line √ 11 y-3 x=(5 √ 77)/3+11 is tangent…

Let the lines $\displaystyle y+2 x=\sqrt{11}+7 \sqrt{7}$ and $\displaystyle 2 y+x=2 \sqrt{11}+6 \sqrt{7}$ be normal to a circle $\displaystyle C:(x-h)^2+(y-k)^2=r^2$. If the line $\displaystyle \sqrt{11} y-3 x=\frac{5 \sqrt{77}}{3}+11$ is tangent to the circle $\displaystyle C$, then the value of $\displaystyle (5 h-8 k)^2+5 r^2$ is equal to \_\_\_\_.