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Math·Geometry and Trigonometry·Circles

hard

A circle in the xy-plane has its center at $(-3,-4)$. Line $k$ is tangent to this circle at the point $(-8,-5)$. What is the slope of line $k$?

A

$-5$

B

$-\frac{1}{5}$

C

$\frac{1}{5}$

D

$5$