Question

what is the standard form of the equation of the circle shown below? a (x - 2)^2+(y - 2)^2 = 16 b (x + 2)^2+(y - 2)^2 = 16 c (x - 2)^2+(y + 2)^2 = 16 d (x + 2)^2+(y + 2)^2 = 16

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: Identify the center of the circle

By observing the graph, the center of the circle is at the point $(- 2,2)$. So $h=-2$ and $k = 2$.

Step3: Identify the radius of the circle

Counting the units from the center of the circle to a point on the circle, we find that the radius $r = 4$ (since $r^2=16$, then $r = 4$).

Step4: Substitute values into the formula

Substitute $h=-2$, $k = 2$, and $r = 4$ into the standard - form equation $(x - h)^2+(y - k)^2=r^2$. We get $(x+2)^2+(y - 2)^2=16$.

Answer:

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