Question

Find an equation for a circle of radius $4$ and center at the point $(0,-2)$.

Short answer

The equation of the circle is$x^2+{(y+2)}^2=16$.

Step-by-step solution

Step 1. Given Information

The radius of the circle is $4$units.

The center of the circle is $(0,-2)$.

We need to find the equation of the circle.

Step 2. Finding the equation of the circle

Equation of a circle with radius $r$units and center at $(h,k)$is given by ${(x-h)}^2+{(y-k)}^2=r^2$.

Here, $h=0,k=-2,r=4$.

Equation of the required circle is:

role="math" localid="1646377000748" $$\begin{gathered} {(x-0)}^2+(y-{(-2))}^2={\left(4\right)}^2 \\ \Rightarrow x^2+{(y+2)}^2=16 \end{gathered}$$