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)

Answer 1

The center of the given circle is at (15, -15), corresponding to option a), and its radius can be expressed as the square root of 57.

Step-by-step explanation:

To find the center and the radius of the circle given by the equation (x - 15)² + (y + 15)² = 57, we can compare it to the standard form of a circle's equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. From the given equation, we can see that h = 15 and k = -15, so the center of the circle is (15, -15), which corresponds to option a). The radius is the square root of 57, which we can write as √57.