Question

what is the equation of a circle with center (-2,1) and radius 6?
a. (x + 2)^2+(y - 1)^2 = 36
b. (x - 2)^2+(y + 1)^2 = 36
c. (x - 2)^2+(y + 1)^2 = 6
d. (x + 2)^2+(y + 1)^2 = 36

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 center $(-2,1)$ and radius $r = 6$, so $h=-2$, $k = 1$, and $r = 6$.

Step3: Substitute values into formula

Substitute $h=-2$, $k = 1$, and $r = 6$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-2))^2+(y - 1)^2=6^2$, which simplifies to $(x + 2)^2+(y - 1)^2=36$.

Answer:

A. $(x + 2)^2+(y - 1)^2=36$