To determine the equation of a circle centered at the origin with a given radius, we'll use the standard form of the equation of a circle.
The general equation for a circle centered at the origin [tex]\((0,0)\)[/tex] with radius [tex]\(r\)[/tex] is given by:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
Here, we know the radius [tex]\( r \)[/tex] is 15.
1. Begin by squaring the radius:
[tex]\[
r^2 = 15^2
\][/tex]
2. Calculate [tex]\( 15^2 \)[/tex]:
[tex]\[
15^2 = 225
\][/tex]
3. Substitute this value back into the general equation:
[tex]\[
x^2 + y^2 = 225
\][/tex]
Thus, the equation of the circle with a radius of 15 centered at the origin is:
[tex]\[ x^2 + y^2 = 225 \][/tex]
Looking at the multiple-choice options, we find the correct answer is:
D. [tex]\( x^2 + y^2 = 225 \)[/tex]
