Question

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

Answer 1

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