Question

The equation of the circle whose center is (0, 0) and radius is length 9 is x² + y² = 3 x² + y² = 9 x² + y² = 81

Answer 1

The equation of a circle with center $(x_0,y_0)$ and radius $r$ is

$(x-x_0)^2 + (y-y_0)^2 = r^2$

In your case, $(x_0,y_0) = (0,0)$ and $r=9$

so the equation becomes

$(x-0)^2 + (y-0)^2 = 9^2 \iff x^2+y^2=81$