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distance formula of a parabola. L 1 2b2 16a2 b2 8 a ln4 a b2 16a2 b L 1 2 b 2 16 a 2 b 2 8 a ln 4 a b 2 16 a 2 b. A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point which is the focus and from a fixed straight line known as the directrix.
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If a 0 then the parabola opens to the right and if a 0 then the parabola opens to the left. Given equation of parabola is y2 12x. Comparing this with the general equation of the parabola y2 4ax.
Given two points x1 y1 and x2 y2 in a rectangular coordinate plane the distance d between them is given by the distance formula d x2 x12 y2 y12.
If you have the equation of a parabola in vertex form y a x h 2 k then the vertex is at h k and the focus is h k 1 4 a. The formula for the arc length of a parabola is. So whats that going to be. Thus the parabola is the set of points equidistant from the line and the focus point.
