Question

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

Answer 1

As equation for the circle is x²+y² = farthest or nearest point's distance
Here its 4
∴ x²+y²=4

Answer 2

It's Radius is 4, that's key (: Knowing the radius is 4 telling you distance from origin.
The equation for a Circle is x^2+y^2.
The farthest it's ever getting from the origin is 4,the closest it's getting to the origin is 4.
Therefore it equals 4(:
x^2+y^2=4 is the base equation.