Which equation represents the polar form of x2 + (y + 4)2 = 16?

Substitute x = r cos(θ) and y = r sin(θ) into the equation. Expanding gives x² + y² + 8y + 16 = 16, so r² + 8r sin(θ) = 0; factoring gives r(r + 8sin(θ)) = 0. The circle is represented by r = −8sin(θ), choice C.

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