In this video I go over the definition of a parabola and then derive the standard formula for parabolas. This is part of my new series on conic sections, or conics, which include parabolas, ellipses ( which includes circles), and hyperbolas because they can be formed by intersecting a plane through a cone (or two cones in the case of a hyperbola).
The definition of a parabola is the series of points that are “equidistant” (or of equal distance) to a fixed point, called the focus point, AND a fixed line, called the directrix. I illustrate this definition and show that we do in fact get the familiar parabolic shape. And when plot this definition onto an x-y plane, and fix the “vertex” of the parabola onto the origin, we can then use Pythagorean theorem to help obtain the standard formula for a parabola: x2 = 4py. Switching the variables x and y to obtain the inverse, we get y2 = 4px.
This is a very important video in understanding exactly how parabolas are defined, which many (including me) have taken for granted and just assumed they were defined as y = a x2; so make sure to watch this video!
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