Final answer:
The center of the circle is (-2, 1), and the radius is √45, which simplifies to 3√5.Circle equation (x + 2)^2 + (y - 1)^2 = 45 in center-radius form with center (-2, 1) and radius 3√5.
Step-by-step explanation:
The equation of a circle in the center-radius form is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius. Given the equation (x + 2)² + (y - 1)² = 45, we can see that it already is in center-radius form. Thus, we can directly read off the center and radius from the equation.
The center is at (h, k) = (-2, 1) because the equation has (x - (-2))² and (y - 1)². The radius is the square root of the number on the right side of the equation, so in this case, r = √45 or r = 3√5.
The circle's equation (x + 2)² + (y - 1)² = 45 is in center-radius form. The center is (-2, 1), derived from (x - (-2))² and (y - 1)². The radius, √45 or 3√5, is obtained from the right side of the equation, providing a clear representation of the circle's properties.