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].
