Parametric Equations

By Taylor Adams

 

In this exploration, we are going to look at different values of a and b for

 

When a=1 and b=1, we get a circle of radius 1.

 

When a=2 and b=2, we get a circle of radius 2.

 

Letís see if a=3 and b=3, if the radius of the produced circle will be 3.

 

What happens if a and b are negative?

When a=-1 and b=-1, it produces the same circle as when a=1 and b=1.

Therefore, when a and be are equal, their absolute value provides the radius of the circle formed.

 

What happens when a and b are not equal?

Letís see what happens when a=2 and b=1.

In this case, the parametric equation produces an oval.The a-value gives us the distance from the origin to the greatest positive x-value, and b gives us the distance from the origin to the greatest positive y-value.

What happens when a=1 and b=2?

This parametric equation is also an oval.The a-value gives us the distance from the origin to the greatest positive x-value, and b gives us the distance from the origin to the greatest positive y-value.

Letís see if a=2 and b=6 will give us the same relationship.

It, in fact, does.In this case, a=2, which is the greatest x-value, and b=6, which is the greatest y-value.

Even though a and b are not equal in these cases, a and b effect the parametric equation in the same way as when they are equal.As I talked about above, a gives us the distance from the origin to the greatest positive x-value, and b gives us the distance from the origin to the greatest positive y-value, which is true whether or not a and be are equal or which value is greater.

 

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