find the equation of the circle shown. write equation in center - radius (or standard) form:

Explanation:

Step1: Identify center coordinates

The center of the circle is at the origin $(0,0)$ as it is symmetric about the x - axis and y - axis and centered on the intersection of the axes.

Step2: Determine radius

The circle intersects the x - axis at $x = 3$ and $x=- 3$, and the y - axis at $y = 3$ and $y = - 3$. So the radius $r = 3$.

Step3: Write the standard - form equation

The standard - form equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$. Substituting $h = 0,k = 0,r = 3$ into the equation, we get $(x-0)^2+(y - 0)^2=3^2$.

Answer:

$x^{2}+y^{2}=9$