The center of a 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 circle’s radius is the distance from the origin to the shared point (0, 9), which is 9. An upward-opening parabola with vertex (0, 9) lies above that vertex for every other x-value, while the circle lies below y = 9 at every other point near its top. So they can intersect only at the vertex, meaning the maximum number of solutions is one.

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