What is the rectangular form of r = −2 sin(θ)?

Use the polar relationships r² = x² + y² and r sin(θ) = y. Multiplying r = −2 sin(θ) by r gives r² = −2r sin(θ), so x² + y² = −2y. Completing the square yields x² + (y + 1)² = 1, which is choice D.

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