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Summary: This module provides practice problems related to developing the formula for an ellipse.
Here is the geometric definition of an ellipse. There are two points called the “foci”: in this case, (-3,0) and (3,0). A point is on the ellipse if the sum of its distances to both foci is a certain constant: in this case, I’ll use 10. Note that the foci define the ellipse, but are not part of it.
The point (
Calculate the distance
Calculate the distance
Now, to create the equation for the ellipse, write an equation asserting that the sum of
Now simplify it. We did problems like this earlier in the year (radical equations, the “harder” variety that have two radicals). The way you do it is by isolating the square root, and then squaring both sides. In this case, there are two square roots, so you will need to go through that process twice.
Rewrite your equation in #3, isolating one of the square roots.
Square both sides.
Multiply out, cancel, combine, simplify. This is the big step! In the end, isolate the only remaining square root.
Square both sides again.
Multiply out, cancel, combine, and get it to look like the standard form for an ellipse.
Now, according to the “machinery” of ellipses, what should that equation look like? Horizontal or vertical? Where should the center be? What are
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This work is licensed by Kenny M. Felder under a Creative Commons Attribution License (CC-BY 2.0), and is an Open Educational Resource.
Last edited by Kenny M. Felder on Dec 31, 2008 7:29 am -0600.
"This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"