The center of the circle is at the origin on a coordinate grid. the vertex of a parabola that opens upward is at (0,9). if the circle intersects the parabola at the parabola's vertex, which statement must be true?

The answer cannot be C or D because the Circle is at the origin on a coordinate grid. So the Circle center is at 0 on the grid. The Circle touches the Parabola at the y coord at 9 and the parabola opens upwards so this tells us the radius of the circle is 9. So if we graph it, the graph would look like the picture below. Since it only touches at one spot, there is only one solution. So the answer is A.