Parametric Equations

Karyn Carson



For various a and b, investigate


LetÕs set a and b equal to a range of values and see what happens and what relationships can be seenÉ


LetÕs begin with situations where a = b and they equal one:


This equation results in a circle with center at the origin and a radius of one.


Now, letÕs change a and b to 2:


ItÕs the same circle.  How can that be? 


LetÕs change a and b to 3:



Same circleÉ


What happens if we make a and b less than one?  How about 0.5?



Aha!  We get a half-circle!  I think this means that if a and b are more than one then the same points are graphed, thereby just going over the previous points.


What if a and b are different?


a=1 and b=2



This is a much different graph!  The limits are still one, but now it looks like a bowÉWhat will happen if a=1 and b=3?


Does b determine the number of sections if a and b arenÕt equal?


a=1, b=4



It would appear soÉat least when a=1.  Now IÕd like to keep b constant and vary aÉ


a=2, b=1


The limit appears still to be one.  I need to look at more graphsÉ


a=3, b=1



This looks just like the graph where a=1 and b=3, but itÕs been turned and visually appears to be centered on the y-axis as opposed to the other graph, which appeared to be centered on the x-axis.  Now a seems to be determining the number of sections.


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