Question

which equation represents a circle with a center at $(-3, -5)$ and a radius of 6 units?$(x - 3)^2 + (y - 5)^2 = 6$$(x - 3)^2 + (y - 5)^2 = 36$$(x + 3)^2 + (y + 5)^2 = 6$$(x + 3)^2 + (y + 5)^2 = 36$

Explanation:

Step1: Recall circle standard equation

The standard form of a circle's equation is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Substitute center $(h,k)=(-3,-5)$

Substitute $h=-3$, $k=-5$ into the formula: $(x-(-3))^2 + (y-(-5))^2 = r^2$, which simplifies to $(x+3)^2 + (y+5)^2 = r^2$.

Step3: Substitute radius $r=6$

Calculate $r^2 = 6^2 = 36$. Substitute into the equation: $(x+3)^2 + (y+5)^2 = 36$.

Answer:

D. $(x + 3)^2 + (y + 5)^2 = 36$