Q3 - Precalculus Enhanced with Graphing Utilities

Question

Graph the equation: $x^2+y^2=9$

Step-by-Step Solution

Answer

The required graph of given equation $x^2+y^2=9$ is as following :-

Step 1. Given Information

We have given the following equation :-

$x^2+y^2=9$

We have to graph this equation.

Firstly we will convert this equation to a general form, then graph it.

Step 2. Compare with general form

The given equation is :-

$x^2+y^2=9$

This equation is of the form ${(x-h)}^2+{(y-k)}^2=r^2$, that is the equation of the circle, where $\left(h,k\right)$ is the center of the circle and $r$ is the radius.

We can write the given equation as following :-

${(x-0)}^2+{(y-0)}^2=3^2$

Now compare this with above general equation of circle, then we have :-

$h=0,k=0 and r=3$.

That is we have to graph a circle with center at origin $(0,0)$ of radius $3$.

Step 3. Graph the circle

Now draw a circle with center at origin $(0,0)$ of radius $3$ units as following :-

This is the required graph.