Question

write the standard form of the equation of the circle with the given center and radius. center (-7,5), r = 8
type the standard form of the equation of the circle
(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 the values of $h$, $k$, and $r$

Given that the center is $(-7,5)$ and $r = 8$, so $h=-7$, $k = 5$, and $r = 8$.

Step3: Substitute the values into the formula

Substitute $h=-7$, $k = 5$, and $r = 8$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-7))^2+(y - 5)^2=8^2$.

Step4: Simplify the equation

$(x + 7)^2+(y - 5)^2=64$.

Answer:

$(x + 7)^2+(y - 5)^2=64$