Eliminate the parameter in the equations x = cos(t) – 5 and y = 3sin(t) + 6. How can the rectangular equation be described?

From x = cos(t) − 5, we get cos(t) = x + 5. From y = 3sin(t) + 6, we get sin(t) = (y − 6)/3. Using cos²(t) + sin²(t) = 1 gives (x + 5)² + (y − 6)²/9 = 1, which is an ellipse, so the answer is B) ellipse.

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