Question

write the standard form of the equation of the circle described below. center (5, - 7), r = 5 the standard form of the equation of the circle is (type an equation. simplify your 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: Identify values of $h$, $k$, and $r$

Given that the center is $(5,-7)$, so $h = 5$, $k=-7$, and $r = 5$.

Step3: Substitute values into the formula

Substitute $h = 5$, $k=-7$, and $r = 5$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 5)^2+(y+7)^2=25$.

Answer:

$(x - 5)^2+(y + 7)^2=25$