Question

the equation of a circle is given below. identify the radius and center. then graph the circle.
$x^{2}+(y + 3)^{2}=25$
radius: 5
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: Rewrite the given equation

The given equation $x^{2}+(y + 3)^{2}=25$ can be written as $(x-0)^{2}+(y-(-3))^{2}=5^{2}$.

Step3: Determine the center and radius

Comparing with the standard form, we have $h = 0$, $k=-3$ and $r = 5$. So the center is $(0,-3)$ and the radius is 5.

Answer:

Radius: 5
Center: (0, - 3)