Question

determine the center and radius of the circle.
$(x + 1)^2 + (y - 4)^2 = 9$
part 1 of 2
the center is $(square, square)$.
part 2 of 2
the radius is $r = square$.

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: Identify $h$ and $k$

Rewrite given equation: $(x - (-1))^2 + (y - 4)^2 = 3^2$.
Here, $h=-1$, $k=4$.

Step3: Identify radius $r$

Match right-hand side to $r^2$: $r^2=9$, so $r=\sqrt{9}=3$.

Answer:

The center is $(-1, 4)$
The radius is $r=3$