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.

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oeerivona oeerivona · Answer 2 · 2021-11-03T19:54:49+01:00

The parabola and the circle have the same axis of symmetry, and can intersect at one point only.

The statement that must be true is; The maximum number of solution is one

Reason:

The given parameters are;

Location of the center of the circle = The origin (0, 0)

Location of the vertex of the parabola opening upwards = (0, 9)

Point where the circle intersects the parabola = The vertex

Required:

The statement that must be true

Solution;

The equation of the circle is x² + y² = r²

The vertex (0, 9) is a point on the circle, therefore;

0² + 9² = r²

The radius, r = 9

The highest point on the circle is the point with the maximum vertical

distance from the center, which is the point (0, 9), which is also the lowest

point on the parabola.

Therefore, the parabola and the circle can intersect at only the point (0, 9),

which gives;

The maximum number of solution is one.

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