Q 5. - Precalculus Enhanced with Graphing Utilities

Question

True or False 

The radius of the circle $x^2+y^2=9$ is $3$.

Step-by-Step Solution

Answer

True

Step 1. Given information

An equation of a circle is $x^2+y^2=9$.

Step 2. State whether the statement is true or false.

In the equation of a circle $x^2+y^2=r^2$

whose center is at the origin, $r$ represents the radius.

Thus, in the equation $x^2+y^2=9$

$\begin{array}{rcl}{r}^2& =& 9\\ r& =& \pm 3\end{array}$ 

The radius is $3$ , since distance cannot be negative.

So, the given statement is true.