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Math·Advanced Math·Nonlinear equations in one variable and systems of equations in two variables

hard

$x^2+y^2=36$

$y=mx+\frac{b}{4}$

In the given system of equations, $m$ and $b$ are negative constants. In the xy-plane, the graphs of the equations in the given system intersect at the point $(-5,y)$, where $y<0$. Which expression represents the value of $b$?

A

$-\frac{5m}{4}+\frac{\sqrt{11}}{4}$

B

$\frac{5m}{4}-\frac{\sqrt{11}}{4}$

C

$-20m+4\sqrt{11}$

D

$20m-4\sqrt{11}$