What is the center of a circle represented by the equation (x−5)2+(y+6)2=42?

A circle in standard form is (x − h)² + (y − k)² = r², and its center is (h, k). Here (x − 5)² gives h = 5, while (y + 6)² = (y − (−6))² gives k = −6. Therefore, the center is (5, −6), choice C.

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