How to find the intersection of a circle and parabola?

Use the substitution method to solve for the system of equations:

Circle: (x-h) ² + (y-k) ² = r²

Parabola: y = a (x-h) ² + k or x = a (y-k) ² + h

(I am using the "y=" parabola for this example)

Substitute a (x-h) ² + k for y into the circle equation and solve for x:

(x-h) ² + [ (a (x-h) ² + k) ² - k]² = r²

Then, substitute that x value into the parabola equation to solve for y.

Hope this makes sense!