The equation of a circle is given by (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius.

The given equation is x² + y² + 8x - 2y - 64 = 0.

To find the center and the radius, we need to rewrite the equation in the form (x-h)² + (y-k)² = r².

First, group the x terms and the y terms:

(x² + 8x) + (y² - 2y) = 64

To complete the square, we take half of the coefficient of x, square it and add it to both sides. We do the same for y:

(x² + 8x + 16) + (y² - 2y + 1) = 64 + 16 + 1

This simplifies to:

(x + 4)² + (y - 1)² = 81

So, the center of the circle is (-4, 1) and the radius is the square root of 81, which is 9.

Therefore, the answer is a. Center: (-4, 1), Radius: 9.

Question

The equation of a circle is given by (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius.

The given equation is x² + y² + 8x - 2y - 64 = 0.

To find the center and the radius, we need to rewrite the equation in the form (x-h)² + (y-k)² = r².

First, group the x terms and the y terms:

(x² + 8x) + (y² - 2y) = 64

To complete the square, we take half of the coefficient of x, square it and add it to both sides. We do the same for y:

(x² + 8x + 16) + (y² - 2y + 1) = 64 + 16 + 1

This simplifies to:

(x + 4)² + (y - 1)² = 81

So, the center of the circle is (-4, 1) and the radius is the square root of 81, which is 9.

Therefore, the answer is a. Center: (-4, 1), Radius: 9.

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