Eliminate the parameter in the equations x is equal to cosine of t minus 5 and y is equal to 3 sine t plus 6 How can the rectangular equation be described?

From x = cos t − 5, we get cos t = x + 5. From y = 3 sin t + 6, we get sin t = (y − 6)/3. Using cos²t + sin²t = 1 gives (x + 5)² + ((y − 6)/3)² = 1, an ellipse with unequal semiaxes 1 and 3, so it is a noncircular ellipse.

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