Question

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

Explanation:

Step1: Identify the center

The center of the circle is at the origin $(0,0)$ as it is symmetrically placed around the intersection of the x - axis and y - axis.

Step2: Determine the 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 equation

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. Since $h = 0,k = 0,r = 3$, the equation is $(x - 0)^2+(y - 0)^2=3^2$, which simplifies to $x^{2}+y^{2}=9$.

Answer:

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