Exploring the Equation of an EllipseLesson Plans > Mathematics > Geometry > Analytic Geometry > Conic Sections > Ellipses
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 x2/a +y2/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:
x2/1 +y2/5 = 1 , a = 1
x2/2 +y2/5 = 1 , a = 2
x2/3 +y2/5 = 1 , a = 3
x2/4 +y2/5 = 1 , a = 4
x2/5 +y2/5 = 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 y2 term? For instance, if the
term under y2 starts at 1 and then increases, predict how the graph will change:
x2/5 +y2/1 = 1 , b = 1
x2/5 +y2/2 = 1 , b = 2
x2/5 +y2/3 = 1 , b = 3
x2/5 +y2/4 = 1 , b = 4
x2/5 +y2/5 = 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?
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