Writing the equation of a circle centered at the origin given its radius or a point on the circle

Question

Give the equation of the circle centered at the origin and passing through the point (0,-4)

Answer 1

The equation of a circle is written like this: (x-a)^2 + (y-b)^2 = r^2, with (a,b) being your center and r being your radius. Since this circle is centered at the origin: (0,0), a and b are zero. So your left side will be (x-0)^2 + (y-0)^2, which simplifies to x^2 + y^2. Your right side is your radius squared (which means multiplied by itself). Here your radius is 4 (as the negative does matter with length), so 4^2 (or 4 x 4) is equal to16.

You are left with x^2 + y^2 = 16

Answer 2

The radius is 4 therefore r^2 = 16 and the equation is

X^2 + Y^2 = 16