Question

determine the center and radius of the circle and sketch the graph. (x - 2)^2=8-(y + 2)^2 the center is (type an ordered pair )

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center and $r$ is the radius. Given $(x - 2)^2=8-(y + 2)^2$, we can rewrite it as $(x - 2)^2+(y + 2)^2=8$.

Step2: Identify the center

Comparing $(x - 2)^2+(y + 2)^2=8$ with $(x - a)^2+(y - b)^2=r^2$, we have $a = 2$ and $b=-2$. So the center of the circle is $(2,-2)$.

Step3: Identify the radius

Since $r^2 = 8$, then $r=\sqrt{8}=2\sqrt{2}$.

Answer:

Center: $(2,-2)$
Radius: $2\sqrt{2}$