Answer:
Option D is correct
[tex]x^2+y^2=4[/tex]
Step-by-step explanation:
The general equation of circle with center (h, k) and radius r is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] ....[1]
As per the statement:
This circle is centered at the origin, and the length of its radius is 2.
Center = (h, k)=(0, 0)
radius(r) = 2 units
Substitute the given values in [1] we have;
[tex](x-0)^2+(y-0)^2=2^2[/tex]
⇒[tex]x^2+y^2=4[/tex]
Therefore, the equation of circle is, [tex]x^2+y^2=4[/tex]
