Articles For Educators

Lesson plans and classroom activities in the areas of mathematics, social studies, lanaguage arts, science, technology, and more.

Share with Other Teachers!

You are here: Directory > Mathematics > Article

Exploring the Equation of an Ellipse

How does the equation of an ellipse relate to its graph?


I Introduce the ellipse concept



"An ellipse looks like an oval. Pretty much a circle that is wider or taller in 1 of its dimensions. You can see pictures

of ellipses here http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php"

II. Exploring the equation and its graph



(To do the following part of the exercise , please open up www.meta-calculator.com, an online graphing calculator that can graph

ellipses. We will explore the way that changing the equation affects the graph of the ellipse)


The general equation of an ellipse looks like x^2/a +y^2/b = 1 .


Now lets explore the roles of each of these 2 variables. First, let's make b =5 and try exploring different values for 'a'

Graph the following equations, making note of the graph of each:

x^2/1 +y^2/5 = 1 , a = 1
x^2/2 +y^2/5 = 1 , a = 2
x^2/3 +y^2/5 = 1 , a = 3
x^2/4 +y^2/5 = 1 , a = 4
x^2/5 +y^2/5 = 1 , a = 5


What effect does increasing 'a'have on the equation ?


Now, take a guess, what do you think will be the effect of changing the variable underneath the y^2 term? For instance, if the

term under y^2 starts at 1 and then increases, predict how the graph will change:


x^2/5 +y^2/1 = 1 , b = 1
x^2/5 +y^2/2 = 1 , b = 2
x^2/5 +y^2/3 = 1 , b = 3
x^2/5 +y^2/4 = 1 , b = 4
x^2/5 +y^2/5 = 1 , b = 5


Ok, was your prediction correct?


Concluding question, in terms of 'a' and 'b', what is true when the ellipse becomes a circle?








Member Comments

Comment by Douglas Twitchell on Dec 30, 2012
Thanks for sharing this lesson plan!

Submit a comment

Please keep comments courteous and on-topic. All comments are moderated by the article author.


Returning Member

Username


Password



Remember me

New Member

Email Address


Username


Password


Confirm Password


  

Common Destinations

Click an icon below for some of the commonly accessed pages at Articles for Educators
Click here to read questions submitted by other teachers, and help them out from your own experiences.
Write up a lesson plan, or just a paragraph or two about your favorite teaching trick.
Articles for Educators provides high quality resources for teachers, administrators and students.

Resource Search


Keep in Touch

It's easy to stay up-to-date; just Like us on Facebook!