Question

the equation of a circle is given below. identify the radius and center. then graph the circle. (x - 3)^2+(y + 4)^2 = 4

Explanation:

Step1: Recall circle - equation form

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: Identify the center

For the equation $(x - 3)^2+(y + 4)^2 = 4$, comparing with the standard form, we have $h = 3$ and $k=-4$. So the center is $(3,-4)$.

Step3: Identify the radius

Since $r^2 = 4$, then $r=\sqrt{4}=2$.

Answer:

Radius: $2$
Center: $(3,-4)$