Question

what is the equation of the circle with a center at (-3, -2) and a radius of 5 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 $(-3,-2)$ and the radius $r = 5$. So, $h=-3$, $k = - 2$, and $r = 5$.

Step3: Substitute the values into the formula

Substitute $h=-3$ into $(x - h)^2$, we get $(x-(-3))^2=(x + 3)^2$. Substitute $k=-2$ into $(y - k)^2$, we get $(y-(-2))^2=(y + 2)^2$. Substitute $r = 5$ into $r^2$, we get $r^2=25$.

Answer:

$(x + 3)^2+(y + 2)^2=25$