Question

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

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

Step3: Identify the radius

Since $r^2 = 4$, taking the square - root of both sides (and considering $r>0$), we get $r = 2$.

Answer:

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