11. $P(4,-5)$ is an external point of the circle $x^{2}+y^{2}=4$. $P A, P B$ are tangents to the circle, then the equation of the line containing the chord $A B$ is $\qquad$ .
11. $4 x-5 y=4$ Hint: It can be proven that: If $P\left(x_{0}, y_{0}\right)$ is an external point of the circle $x^{2}+y^{2}=r^{2}$, and tangents are drawn from $P$ to the circle, with $A$ and $B$ being the points of tangency, then the equation of the line $AB$ is $x_{0} x+y_{0} y=r^{2}$.