Identify the center and radius of the circle written in standard form.
x^2 + (y + 3)^2 = 8
center (x, y) = (0,-3)
radius = 2 square root 2
please check answer if correct
radius
correct
To identify the center and radius of the circle written in standard form, we need to compare the equation to the standard form equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2.
The given equation x^2 + (y + 3)^2 = 8 can be rewritten as (x - 0)^2 + (y + 3)^2 = (2√2)^2.
From this, we can determine that the center of the circle is (h, k) = (0, -3), because the x-coordinate is 0 and the y-coordinate is -3.
The radius of the circle is determined by taking the square root of the value on the right side of the equation. In this case, the radius is 2√2.
Therefore, the center of the circle is (0, -3) and the radius is 2√2.