# Find the vertex focus and directrix of the parabola calculator

## Finding the vertex, focus and directrix of a parabola

How to find the foci, center and vertices, and asymptotes of a hyperbola

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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. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.

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

Account Options Sign in. Top Charts. New Releases. Parabola Solver Sir Sagar Education. Add to Wishlist. Parabola solver helps the users to find different attributes of the parabola by providing the parabola equation in vertex , standard or intercept forms.

## Parabola Graph and Equation

Finding The Focus and Directrix of a Parabola

## Focus & directrix of a parabola from equation

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 :. Here, the distance between the point and horizontal line is difference of their y -coordinates.

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This calculator will find either the equation of the parabola from the given eccentricity, latus rectum, length of the latus rectum, focus, vertex, directrix, focal.
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If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Precalculus Conic sections Focus and directrix of a parabola. Next lesson. Current timeTotal duration Focus and directrix of a parabola conic sections. Video transcript - This right here is an equation for a parabola and the role of this video is to find an alternate or to explore an alternate method for finding the focus and directrix of this parabola from the equation.

Any time you come across a quadratic formula you want to analyze, this parabola calculator will be the perfect tool for you. Not only will it provide you with the parabola equation in the standard form and vertex form, but also calculate the parabola vertex, focus and directrix. Parabola is a U-shaped symmetrical curve. Its main property is that every point lying on a parabola equidistant from both a certain point, called the focus of a parabola, and a line, called its directrix. It is also the curve that corresponds to quadratic equations.

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## 4 thoughts on “Find the vertex focus and directrix of the parabola calculator”

1. Jafugoco says:

Parabola- Graph, Equation, Axis of Symmetry, Focus , Directrix and more

2. Nylpblutoutin says:

Parabola Calculator - eMathHelp