Questions: The equation of a circle is given in standard form. Complete parts a through c to follow the step by step process to sketch the graph of the circle. [ x^2+(y-4)^2=16 ] a) Determine the center and radius of the circle. The center of the circle is (Type an ordered pair.)

Solution Steps

The equation of the circle is given in the standard form: \[ x^{2}+(y-4)^{2}=16 \] The standard form of a circle's equation is: \[ (x-h)^{2} + (y-k)^{2} = r^{2} \] where \((h, k)\) is the center and \(r\) is the radius.

Comparing the given equation with the standard form, we find:

• \(h = 0\)
• \(k = 4\)

Thus, the center of the circle is \((0, 4)\).

From the equation: \[ x^{2}+(y-4)^{2}=16 \] we have \(r^{2} = 16\).

Taking the square root of both sides, we find: \[ r = \sqrt{16} = 4 \]

Final Answer