Question

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.)
the radius is
(simplify your answer. type an exact answer, using radicals as needed.)
b) sketch the graph of the circle.
use the graphing tool to graph the circle
click to enlarge graph
c) determine the x - and y - intercepts of the circle. select the correct choice and, if necessary, fill in the answer box within your choice.
a. the x - intercept(s) is/are x =
(use a comma to separate answers as needed. type an exact answer, using radicals as needed.)

Explanation:

Answer:

(a) Center: \( (0,4) \); Radius: \( 4 \)
(b) Plot the center at \((0,4)\) on the coordinate - plane. Then, from the center, mark points 4 units up, down, left, and right and draw a smooth circle passing through these points. Label the \(x\) - axis and \(y\) - axis.
(c) \(x\) - intercepts: \(x = \pm\sqrt{16 - 16}=0\); \(y\) - intercepts: Set \(x = 0\), then \((y - 4)^{2}=16\), \(y-4=\pm4\), \(y = 0,8\)