Question

the graph of a circle with center (x, y) = (5, 7) is shown below. write the equation for the circle. resources master it

Explanation:

Step1: Recall circle - equation formula

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.

Step2: Identify the center coordinates

Given the center $(h,k)=(5,7)$, so $h = 5$ and $k = 7$.

Step3: Determine the radius

By observing the graph, the radius $r = 2$.

Step4: Substitute values into the formula

Substitute $h = 5$, $k = 7$, and $r = 2$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 5)^2+(y - 7)^2=4$.

Answer:

$(x - 5)^2+(y - 7)^2=4$