Q. 13 - Precalculus Enhanced with Graphing Utilities

Question

Graph each equation.

$x^2+{\left(y-3\right)}^2=16$

Step-by-Step Solution

Answer

On graphing the equation, we get,

Step 1. Given information.

Consider the given question,

$x^2+{\left(y-3\right)}^2=16 ...... \left(i\right)$

The equation of a circle with center $\left(h,k\right)$ and radius r is given below,

${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2 ...... \left(ii\right)$

Compare equations (i) and (ii),

$$\begin{gathered} h=0, \\ k=3, \\ r=4 \end{gathered}$$

Then the center of the circle is at $\left(h,k\right)=\left(0,3\right)$.

As the radius is $4$ units, four points on the circle can be located by plotting points that are $4$ units to the right, left, up and down from the center.

Step 2. Plot the graph.

On plotting the graph,