Question

write the standard form of the equation of the circle with the given center and radius.
center $(-3,5)$, $r=6$
type the standard form of the equation of the circle.
(simplify your answer.)

Explanation:

Step1: Recall circle standard form

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

Step2: Substitute center values

Here, $h=-3$, $k=5$. Substitute into the formula:
$(x - (-3))^2 + (y - 5)^2 = r^2$
Simplify the first term: $(x+3)^2 + (y-5)^2 = r^2$

Step3: Substitute radius value

$r=6$, so $r^2=6^2=36$. Substitute this in:
$(x+3)^2 + (y-5)^2 = 36$

Answer:

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