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 maximum number of solutions is one.
The maximum number of solutions is three.
The circle has a radius equal to 3.
The circle has a radius less than 9.

Question

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 maximum number of solutions is one.
The maximum number of solutions is three.
The circle has a radius equal to 3.
The circle has a radius less than 9.

mathmate · Answer

As in all geometry problems, start with a diagram.
Can you draw a diagram to illustrate the problem?