Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

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:

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