thus our two curves are:
and we want these two curves to have only two points in common. (it is okay to take this interpretation since the circle will be "inside" the parabola)
plug in into the equation of the circle, we get:
the above is quadratic in
we want this to have only two solutions, therefore, set the discriminant to zero.
thus, it remains for us to solve:
knowing the value for , we plug it into equation (1) to find the x-coordinate for the point of intersection. then use that to get the y-coordinate. (note, one of your solutions for y will be erroneous, be sure to make sure your solutions work in BOTH of the original equations). i leave the rest to you, it's pretty much following your nose from here