Explanation:
the equation of a circle centered at the origin is
x² + y² = r²
r being the radius (the distance of the center to every point on the circle's arc).
so, we get a point on the arc : (0, -5).
what is its distance to the origin ?
the origin is (0, 0).
we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.
that means there is no distance between them in x direction.
the only distance is in y direction : 0 to -5.
a distance is always positive (no matter in what direction).
so, the distance from 0 to -5 is : 5 units.
that means r = 5.
and our equation is
x² + y² = 5² = 25