Question

write the equation of this circle in standard form.

Explanation:

Step1: Identify center coordinates

The center of the circle is at the origin $(0,0)$.

Step2: Determine radius

The radius $r$ is the distance from the center $(0,0)$ to a point on the circle. From the graph, $r = 8$.

Step3: Write standard - form equation

The standard - form equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. Substituting $h = 0$, $k = 0$, and $r = 8$ gives $(x - 0)^2+(y - 0)^2=8^2$, which simplifies to $x^{2}+y^{2}=64$.

Answer:

$x^{2}+y^{2}=64$