what is the standard form of the equation of the circle shown below?\na $(x - 2)^2+(y - 2)^2 = 16$ b $(x +…

what is the standard form of the equation of the circle shown below?\na $(x - 2)^2+(y - 2)^2 = 16$ b $(x + 2)^2+(y - 2)^2 = 16$\nc $(x - 2)^2+(y + 2)^2 = 16$ d $(x + 2)^2+(y + 2)^2 = 16$

what is the standard form of the equation of the circle shown below?\na $(x - 2)^2+(y - 2)^2 = 16$ b $(x + 2)^2+(y - 2)^2 = 16$\nc $(x - 2)^2+(y + 2)^2 = 16$ d $(x + 2)^2+(y + 2)^2 = 16$

Answer

Explanation:

Step1: Recall circle - equation formula

The standard form of the 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: Determine the center and radius from the graph

From the graph, the center of the circle is at the point $(2,2)$ and the radius $r = 4$ (since the distance from the center to the edge of the circle is 4 units). Here $h = 2$, $k = 2$, and $r^2=16$.

Step3: Write the equation of the circle

Substitute $h = 2$, $k = 2$, and $r^2 = 16$ into the standard - form equation: $(x - 2)^2+(y - 2)^2=16$.

Answer:

A. $(x - 2)^2+(y - 2)^2=16$