A parabola is a U-shaped curve. The intersection of a cone and a plane parallel to the slant height of the cone is parabolic. A quadratic relation forms a parabola, but it can also be defined independently of this.
A Focus and a horizontal Directrix
A parabola is the set of all points that are the same distance from a given point \(F(a, b)\) and a given line \(y = c\). The given point is called the \(Focus\), and the line the \(Directrix\).
An interesting property you can explore using the link above is that light from an infinite source will always be reflected to the Focus.
A Focus and any Directrix
A parabola is the set of all points that are the same distance from a given point \(F(a, b)\) and a given line \(y = cx+d\). The given point is called the Focus, and the line the Directrix.
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