This circle is centered at the origin, and the length of its radius is 4. what is
the equation of the circle?

D. x² + y² = 4²

Step-by-step explanation:

The general equation of a circle is given in the attached  graphic.

In this case, we can see that the center of the circle is at the origin i.e (0,0) and that the radius is 4 units.

the values for h, k and r in the general equation are as follows:

h = 0, k=0, r = 4

putting this into the general equation:

(x-h)² + (y-k)² = r²

(x-0)² + (y-0)² = 4²

x² + y² = 4²