Question

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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: 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 of the circle

From the graph, the center of the circle is at the point $(- 7,-5)$. So $h=-7$ and $k = - 5$.

Step3: Determine the radius of the circle

The radius $r = 2$.

Step4: Substitute values into the formula

Substitute $h=-7$, $k=-5$, and $r = 2$ into the standard - form equation: $(x-(-7))^2+(y - (-5))^2=2^2$, which simplifies to $(x + 7)^2+(y + 5)^2=4$.

Answer:

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