Question

find an equation of the circle having the given graph. express the equation in standard form. the equation of the circle is (type an equation. type your answer in standard form. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Identify the center of the circle

By observing the graph, the center of the circle $(h,k)$ is at $(0,0)$.

Step2: Identify the radius of the circle

Counting the grid - squares, the radius $r$ is 5.

Step3: Use the standard form of the circle equation

The standard form of a circle equation is $(x - h)^2+(y - k)^2=r^2$. Substituting $h = 0$, $k = 0$, and $r = 5$ into the equation, we get $(x-0)^2+(y - 0)^2=5^2$.

Answer:

$x^{2}+y^{2}=25$