Intersection of a Circle and Parabola

To see how many ways we can intersect two circles, try adjusting the [color=#ff0000]red parabola[/color] above to see how many times it can meet the [color=#0000ff]blue circle[/color].[br]You can drag the vertex, [math]V[/math], and focus, [math]F[/math], around to change the location and shape of the parabola.
What is the maximum number of points of intersection?
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Information: Intersection of a Circle and Parabola