If the asymptotes of the hyperbola $9x^2-4y^2-18x-24y-63=0$ are  tangents to the circle$13x^2+13y^2-26x+k=0$  at point $A({\alpha }_1,{\beta }_1)$ and  $B({\alpha }_2,{\beta }_2)$ then   $|{\alpha }_1+{\alpha }_2+k|$ is equal to

Asymptotes 3(x – 1) – 2(y + 3) = 0 and 3(x – 1) + 2(y + 3) = 0
3x – 2y – 9 = 0 and 3x + 2y + 3 = 0
It touches  $x^2+y^2-2x+k/13=0$
$\therefore A(-\frac{5}{13},-\frac{12}{13})andB(\frac{31}{13},-\frac{12}{13})$
$\therefore k=-23$