Question

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

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the center

For the equation $x^{2}+(y - 4)^{2}=4$, comparing with the standard - form $(x - a)^2+(y - b)^2=r^2$, we have $a = 0$ and $b = 4$. So the center is $(0,4)$.

Step3: Identify the radius

Since $r^{2}=4$, taking the square - root of both sides (and considering $r>0$ as it represents a radius), we get $r = 2$.

Answer:

Radius: $2$
Center: $(0,4)$