Question

Find the center and the radius of the given circle: ((x - 15)^2 + (y + 15)^2 = 57).

Center:
A. (15, -15)
B. (15, 15)
C. (-15, -15)
D. (-15, 15)
Radius:
A. 3
B. (sqrt{57})
C. 6
D. 8

Answer 1

The center of the given circle is (15, -15) and the radius is √57.

Step-by-step explanation:

The given equation of the circle is (x - 15)^2 + (y + 15)^2 = 57. To find the center and radius, we can compare the equation to the standard form of a circle, which is (x - h)^2 + (y - k)^2 = r^2.

Comparing the equations, we can determine that the center of the circle is (h, k) = (15, -15) and the radius (r^2) = 57. Taking the square root of both sides gives us the radius r = √57, which is approximately 7.55.

Therefore, the center of the circle is (15, -15) and the radius is approximately 7.55.

So the correct answers are A. (15, -15) and B. √57.