Which equation represents a circle with center (4, -1) and radius 5?

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Multiple Choice

Which equation represents a circle with center (4, -1) and radius 5?

Explanation:
The equation of a circle in standard form is (x − h)^2 + (y − k)^2 = r^2, where the center is (h, k) and the radius is r. Here, the center is (4, −1) and the radius is 5. Plugging in gives (x − 4)^2 + (y − (−1))^2 = 5^2, which simplifies to (x − 4)^2 + (y + 1)^2 = 25. Other options would place the center at different coordinates or give a different radius, so they don’t match the given center and radius.

The equation of a circle in standard form is (x − h)^2 + (y − k)^2 = r^2, where the center is (h, k) and the radius is r.

Here, the center is (4, −1) and the radius is 5. Plugging in gives (x − 4)^2 + (y − (−1))^2 = 5^2, which simplifies to (x − 4)^2 + (y + 1)^2 = 25.

Other options would place the center at different coordinates or give a different radius, so they don’t match the given center and radius.

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