What is the radius of the circle defined by the equation [tex][tex]$x^2 + y^2 = 9$[/tex][/tex]?

A. [tex]-3[/tex]
B. [tex]3[/tex]
C. [tex]3[/tex] and [tex]-3[/tex]
D. [tex]9[/tex]
E. [tex]-9[/tex]



Answer :

To find the radius of the circle defined by the equation [tex]\( x^2 + y^2 = 9 \)[/tex], let's break down the steps.

1. Understand the Equation of a Circle:
The general form of the equation of a circle is given by:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.

2. Compare with the Given Equation:
The given equation is:
[tex]\[ x^2 + y^2 = 9 \][/tex]

3. Identify [tex]\( r^2 \)[/tex]:
By comparing the given equation with the general form, we can see that:
[tex]\[ r^2 = 9 \][/tex]

4. Solve for the Radius [tex]\( r \)[/tex]:
To find the radius, we take the square root of both sides of the equation [tex]\( r^2 = 9 \)[/tex]:
[tex]\[ r = \sqrt{9} \][/tex]

5. Calculate the Square Root:
The square root of 9 is 3. Therefore, the radius [tex]\( r \)[/tex] is:
[tex]\[ r = 3 \][/tex]

Thus, the radius of the circle defined by the equation [tex]\( x^2 + y^2 = 9 \)[/tex] is [tex]\( 3 \)[/tex].