Consider the circle C: x^2+y^2-6 x-8 y-11=0. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of…

Consider the circle C : $\displaystyle x^2+y^2-6 x-8 y-11=0$. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle $\displaystyle x^2+y^2-\alpha x-\beta y-\gamma=0$, then $\displaystyle \alpha+\beta+2 \gamma$ is equal to $\displaystyle \_\_\_\_$.