Derivating Standard Equation: Ellipse

Do you want to know from where we get the equation for the ellipses in Standard Form? Ellipses like the parabolas and the hyperbolas get their equation derivated using the distance formula and complying with the "locus" defining the corresponding geometric space. In the case of the ellipse this is defined as the sum of the distances from two points called foci to a point in the ellipse geometric space. This sum has to remain constant for the the definition to be true. This lesson will walk you through the proof with a lot of visuals to help you in obtaining the equation in Standard Form for ellipses using the Distance Formula. The proof does not provide practice problems but you may interact with it using the MARKER TOOLS menu located at the upper right corner of the screen and once the proof has started you may predict the following steps on the screen before the proof is run.

At the end of the lesson you are given a real world application problem that dwells with how the epicenter of an earthquake is determined with the report of at least 3 seismic stations. The aim of this lesson is to present the ellipse showing each one of the involved steps; including how you have to complete the square, and how you need to factor perfect square trinomials. You will view problems that go from the equation to the graph, and vice versa. Struggling students find it very friendly and constructive, advanced students find it challenging interesting!

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary



All sections generated by performing transversal cuts to a right cone.


The geometric space that is equidistant from a line called the directrix and a point of a parpendicular to this calle the focus.


The abolute value sum of the distances from two fixed points called focii and a geometric space for which this sum remains constant.


The absolute value difference of two points called focii and a a geometric space for which this difference remains constant.


A geometric space that is equidistant from a point called center.


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