Question

writing an equation with a given center and radius
which equation represents a circle with a center at (2, -8) and a radius of 11?
(x - 8)^2+(y + 2)^2 = 11
(x - 2)^2+(y + 8)^2 = 121
(x + 2)^2+(y - 8)^2 = 11
(x + 8)^2+(y - 2)^2 = 121

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 the center $(2,-8)$, so $h = 2$ and $k=-8$. The radius $r = 11$.

Step3: Substitute values into the formula

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

Answer:

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