Question

find the standard form of the equation for the following circle.

Explanation:

Step1: Identify the center of the circle

From the graph, the center of the circle $(h,k)$ is $(- 2,1)$.

Step2: Determine the radius of the circle

Count the distance from the center to a point on the circle. The radius $r = 3$.

Step3: Use the standard - form equation of a circle

The standard - form equation of a circle is $(x - h)^2+(y - k)^2=r^2$. Substitute $h=-2$, $k = 1$, and $r = 3$ into the equation.
We get $(x+2)^2+(y - 1)^2=9$.

Answer:

$(x + 2)^2+(y - 1)^2=9$