State the center and the radius of the circle represented by the equation
(x – 8) 2 + (y + 2)2 = 81
Eq: (x - h)2 + (y - k)^2 = r^2.
C(h , k), r = sqrt(r^2).
(x - 8)^2 + (y + 2)^2 = 81.
C(h , k) = C(8 , -2).
r = sqrt(r^2) = sqrt(81) = 9.
To identify the center and radius of the circle represented by the equation (x – 8)^2 + (y + 2)^2 = 81, we can apply the standard form of the equation for a circle, which is (x – h)^2 + (y – k)^2 = r^2.
Comparing the given equation to the standard form, we can infer that the center of the circle is at the point (h, k), where h = 8 and k = -2.
Therefore, the center of the circle is (8, -2).
To determine the radius, we can take the square root of the value on the right side of the equation, r^2 = 81, which gives us r = √81 = 9.
Hence, the radius of the circle represented by the equation is 9.