Question

find the center and the radius of the circle. then graph the circle.
( x^2 = 16 - (y + 5)^2 )
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use the graphing tool to graph the circle.
click to enlarge graph
(coordinate grid image with x-axis from -10 to 10 and y-axis from -10 to 10)

Explanation:

Step1: Recall the standard circle equation

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.

Step2: Rearrange the given equation

Start with \(x^2 = 16 - (y + 5)^2\).
Add \((y + 5)^2\) to both sides: \(x^2 + (y + 5)^2 = 16\).
Rewrite \(x^2\) as \((x - 0)^2\) and \(16\) as \(4^2\): \((x - 0)^2 + (y - (-5))^2 = 4^2\).

Answer:

The center of the circle is \((0, -5)\) and the radius is \(4\).