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!