To determine the equation of a circle centered at the origin with a given radius, we can use the standard form of the equation for a circle. The general form for the equation of a circle centered at the origin [tex]\((0,0)\)[/tex] with a radius [tex]\(r\)[/tex] is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
We are given that the radius [tex]\(r\)[/tex] of the circle is 12. Plugging this value into the equation, we get:
[tex]\[ r = 12 \][/tex]
Substitute [tex]\(r\)[/tex] with 12 in the standard form equation:
[tex]\[ x^2 + y^2 = 12^2 \][/tex]
Now, compute [tex]\(12^2\)[/tex]:
[tex]\[ 12^2 = 144 \][/tex]
Therefore, the equation of the circle centered at the origin with a radius of 12 is:
[tex]\[ x^2 + y^2 = 144 \][/tex]
Thus, the correct answer is:
D. [tex]\(x^2 + y^2 = 144\)[/tex]
