Question

determine the center and radius of the circle.
$(x - 4)^2 + (y + 1)^2 = 64$
part 1 of 2
the center is (4, \square).
part 2 of 2
the radius is $r = 8$.

Explanation:

Step1: Recall circle standard form

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

Step2: Match given equation to standard form

Given equation: $(x-4)^2+(y+1)^2=64$, rewrite as $(x-4)^2+(y-(-1))^2=8^2$.

Step3: Identify center coordinates

Compare to standard form: $h=4$, $k=-1$.

Step4: Identify radius value

Compare to standard form: $r^2=64$, so $r=\sqrt{64}=8$.

Answer:

Part 1: The center is $(4, -1)$
Part 2: The radius is $r=8$