Question

a) find the center - radius form of the equation of the circle with center (0,0) and radius 13.
b) graph the circle.
a) the center - radius form of the equation of the circle is (type an equation.)

Explanation:

Step1: Recall the center - radius form of a circle's equation

The center - radius form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Substitute the given values into the formula

Given that the center \((h,k)=(0,0)\) and radius \(r = 13\). Substitute \(h = 0\), \(k = 0\), and \(r=13\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x - 0)^2+(y - 0)^2=13^2\).

Answer:

\(x^{2}+y^{2}=169\)