Give the equation of the circle centered at the origin and passing through the point (0, -11).

answer

x^2 + y^2 = 121

set up equation

the equation of a circle is (x - h)^2 + (y - k)^2 = r^2

where h is the center x coordinate and k is the center y coordinate

values

from the origin (0, 0) we know that h = 0 and k = 0

since the circle passes through (0, -11) the distance from the origin is 11

r =11

r^2 = 121

plug in values

now that we have all the values, we plug them into (x - h)^2 + (y - k)^2 = r^2

(x - h)^2 + (y - k)^2 = r^2

(x - 0)^2 + (y - 0)^2 = 121

x^2 + y^2 = 121