Question

the equation of a circle is given below.
$(x - 0.5)^2 + (y - 3.5)^2 = 16$
what is its center?
( , )
what is its radius?
if necessary, round your answer to two decimal places.
units
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Explanation:

Step1: Recall the standard form of a circle's 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: Identify the center

For the equation \((x - 0.5)^2+(y - 3.5)^2 = 16\), comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 0.5\) and \(k=3.5\).

Step3: Identify the radius

Since \(r^2 = 16\), then \(r=\sqrt{16}\).

Answer:

Center: \((0.5,3.5)\)
Radius: \(4\) units