What is the radius of the circle x^2+y^2-4y=21 7 Write your answer in simplified, rationalized form. square

To find the radius of the circle given by the equation , we need to rewrite the equation in the standard form of a circle's equation, which is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and is the radius.First, let's complete the square for the -terms in the given equation: We focus on the -terms: . To complete the square, we add and subtract the square of half the coefficient of : Now substitute this back into the original equation: Add 4 to both sides to isolate the completed square term: This is now in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where , , and . Therefore, the radius is: So, the radius of the circle is .