Question

write the standard form of the equation of the circle with the given center and radius. center (-6,8), r = 10 type the standard form of the equation of the circle. (simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

The standard - form 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 $(-6,8)$, so $h=-6$, $k = 8$, and $r = 10$.

Step3: Substitute values into the formula

Substitute $h=-6$, $k = 8$, and $r = 10$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-6))^2+(y - 8)^2=10^2$.

Step4: Simplify the equation

$(x + 6)^2+(y - 8)^2=100$.

Answer:

$(x + 6)^2+(y - 8)^2=100$