Conic Sections: The Parabola

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In this lesson, we will learn about the geometric definition of a parabola. A parabola is the set of all points that are equidistant from a fixed point called the focus and a fixed line called the directrix. The distance from the vertex to the focus is normally labeled as p and gives us two equations to work with: (x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h), these equations will change when we open down or left, we will have a negative p in these cases: (x - h)2 = -4p(y - k) or (y - k)2 = -4p(x - h). To solve these types of problems, we will calculate the distance from the vertex to the focus, this will give us our p-value. We will then plug in for h, k, and p and simplify.
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