Question

what is the equation of the circle with a center at (-6, 8) and a radius of 11 units? 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: Identify the values of $h$, $k$, and $r$

Given that the center is $(-6,8)$ and the radius $r = 11$. Here $h=-6$, $k = 8$, and $r = 11$.

Step3: Substitute the values into the formula

Substituting $h=-6$, $k = 8$, and $r = 11$ into $(x - h)^2+(y - k)^2=r^2$, we get $(x-(-6))^2+(y - 8)^2=11^2$, which simplifies to $(x + 6)^2+(y - 8)^2=121$.

Answer:

$(x+6)^2+(y - 8)^2=121$