Give the equation of the circle centered at the origin and passing through the point , 0−3 .

X^2 + y^2 = 9  
The general equation for a circle of radius r centered at point (h,k) is 
(x - h)^2 + (y - k)^2 = r^2  
Since we want it centered at the original, h and k are both 0, so the equation simplifies to: 
x^2 + y^2 = r^2 
 Substituting the known values for the given point gives: 
x^2 + y^2 = r^2
 0^2 + 3^2 = r^2
 0 + 9 = r^2
 9 = r^2
 3 = r
 
 So we have
 x^2 + y^2 = 3^2
 or
 x^2 + y^2 = 9