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Chapter 1: Q 5. (page 50)

True or False
The radius of the circle $x^{2} + y^{2} = 9$ is $3$ .

Short Answer

Expert verified

True

Step by step solution

01

Step 1. Given information

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

02

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.

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