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Math·Geometry and Trigonometry·Circles

hard

A circle in the $xy$-plane has its center at $(-4,-7)$. Line $k$ is tangent to this circle at the point $(-7,-8)$. What is the slope of line $k$?

A

$-3$

B

$-\frac{1}{3}$

C

$\frac{1}{3}$

D

$3$