To find the equation of a circle centered at the origin (0, 0) with a given radius, we use the general equation of a circle:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
where \( r \) is the radius of the circle.
1. We are given that the radius \( r \) is 2.
2. Substitute \( r = 2 \) into the equation:
[tex]\[ x^2 + y^2 = 2^2 \][/tex]
3. Calculate \( 2^2 \):
[tex]\[ 2^2 = 4 \][/tex]
4. Therefore, the equation of the circle is:
[tex]\[ x^2 + y^2 = 4 \][/tex]
Let's match this result with the given options:
A. \( x^2 + y^2 = 2 \) — Incorrect
B. \( x^4 + y^4 = 4 \) — Incorrect
C. \( x^2 + y = 2 \) — Incorrect
D. \( x^2 + y^2 = 4 \) — Correct
Hence, the correct answer is:
D. [tex]\( x^2 + y^2 = 4 \)[/tex]
