which equation represents a circle with a center at (-3, -5) and a radius of 6 units?\n(x - 3)^2+(y - 5)^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 $(-3,-5)$, so $h=-3$, $k = - 5$, and the radius $r = 6$.

Step3: Substitute the values into the formula

Substitute $h=-3$, $k=-5$, and $r = 6$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-3))^2+(y - (-5))^2=6^2$, which simplifies to $(x + 3)^2+(y + 5)^2=36$.

Answer:

$(x + 3)^2+(y + 5)^2=36$ (corresponding to the fourth option in the multiple - choice list)