Question

determine the center and radius of the circle.
$(x - 4)^{2}+(y - 8)^{2}=9$
a) center: $(4,8)$
radius: 3
b) center: $(4,8)$
radius: 9
c) center: $(-4,-8)$
radius: 3
d) center: $(-4,-8)$
radius: 9

Explanation:

Step1: Recall the standard form of a 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: Identify the center

For the equation \((x - 4)^2+(y - 8)^2 = 9\), comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 4\) and \(k = 8\). So the center \((h,k)=(4,8)\).

Step3: Identify the radius

Since \(r^2=9\), then \(r=\sqrt{9}=3\) (we take the positive value as radius is non - negative).

Answer:

A. Center: \((4,8)\), Radius: \(3\)