Give the center and radius of each circle and graph.
$x^2+y^2=36$

• A. $r=6$; Center: $(6,0)$
• B. $r=6$; Center: $\left(0,0\right)$
• C. $r=6$; Center: $\left(6,0\right)$
• D. $r=6$; Center: $\left(0,0\right)$

Answer: (B)

Verified step by step guidance

1. Identify the general form of the equation of a circle: \(\left(x - h\right)^2 + \left(y - k\right)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.
2. Look at the given equation \(x^2 + y^2 = 36\). Notice that it matches the general form with \(h = 0\) and \(k = 0\), so the center is at the origin \((0,0)\).
3. Determine the radius by taking the square root of the constant on the right side of the equation: \(r = \sqrt{36}\).
4. From the graph, confirm that the circle is centered at \((0,0)\) and passes through points such as \((6,0)\), \((0,6)\), \((-6,0)\), and \((0,-6)\), which verifies the radius is 6.
5. To graph the circle, plot the center at \((0,0)\) and mark points 6 units away in all directions (up, down, left, right), then draw a smooth curve connecting these points to form the circle.