Question

what is the equation of the circle? enter an answer in each box to complete the equation. be sure to include a plus or minus symbol where needed. (x )^2+(y )^2=

Explanation:

Step1: Identify center and radius

The standard - form equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius. From the graph, the center of the circle is $(10,10)$ and a point on the circle is $(10,22)$. The radius $r$ is the distance between the center $(10,10)$ and the point $(10,22)$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, here $x_1 = 10,y_1 = 10,x_2 = 10,y_2 = 22$, so $r=\sqrt{(10 - 10)^2+(22 - 10)^2}=12$.

Step2: Write the equation of the circle

Substitute $h = 10,k = 10,r = 12$ into the standard - form equation of a circle. We get $(x - 10)^2+(y - 10)^2=144$.

Answer:

$(x - 10)^2+(y - 10)^2=144$