# Find the vertex focus and directrix of the parabola calculator

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## Focus of a Parabola

Free Parabola Directrix calculator - Calculate parabola directrix given equation step-by-step.

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A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix. The focus lies on the axis of symmetry of the parabola. Notice that here we are working with a parabola with a vertical axis of symmetry, so the x -coordinate of the focus is the same as the x -coordinate of the vertex. The focus is at 0 , 2.

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You will also need to work the other way, going from the properties of the parabola to its equation. The vertex is always halfway between the focus and the directrix, and the parabola always curves away from the directrix, so I'll do a quick graph showing the focus, the directrix, and a rough idea of where the parabola will go:. The absolute value of p is the distance between the vertex and the focus and the distance between the vertex and the directrix. The sign on p tells me which way the parabola faces. Since this is a "sideway" parabola, then the y part gets squared, rather than the x part. So the conics form of the equation must be:. And that's all I need for my equation, since they already gave me the vertex.

Given the focus and directrix of a parabola , how do we find the equation of the parabola? Let x 0 , y 0 be any point on the parabola. Any point, x 0 , y 0 on the parabola satisfies the definition of parabola, so there are two distances to calculate:. To find the equation of the parabola, equate these two expressions and solve for y 0. Distance between the point x 0 , y 0 and a , b :.

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