Answer
$y=-\sqrt{36-x^2}$
Work Step by Step
The equation of the bottom half of the circle can be found by taking the equation of the circle and excluding all of the positive y-values. In order to see how this works let's rewrite the equation:
$x^2+y^2=36$
$y^2=36-x^2$
$y=±\sqrt{36-x^2}$
After taking the square root of both sides, we can see that see that the equation of the circle has both positive and negative y-values. Let's remove the positive sign to end up with only the bottom half of the circle.
$y=-\sqrt{36-x^2}$
