Questions: Find the center, radius, and intercepts of the circle given below and then sketch the graph of the circle. x^2+(y-9)^2=81 The center of the circle is (Type an ordered pair.)

The given equation of the circle is: \[ x^{2}+(y-9)^{2}=81 \]

This is in the standard form of a circle equation: \[ (x-h)^{2} + (y-k)^{2} = r^{2} \]

Comparing the given equation with the standard form, we can identify:

• The center \((h, k)\) is \((0, 9)\).
• The radius \(r\) is \(\sqrt{81} = 9\).

To find the intercepts, we need to determine where the circle intersects the x-axis and y-axis.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 20}, "commands": ["(x2) + ((y-9)2) - 81"], "latex_expressions": ["$x^{2}+(y-9)^{2}=81$"]}