Parametric Equations

By: Lacy Gainey


Graph the parametric equations

I would recommend using graphing calculator software (such as Graphing Calculator 3.4 or 4), so you can more easily observe the parametric curves.

Notice that the parametric equations produced a circle with a radius of 1.

Up until this point, students may have only been exposed to this equation of a circle: [1 GSP], where the circle is centered at the origin and r is the radius of the circle. 

In a right triangle, recall that .  In the diagram, we are letting t = θ. t is our parameter.


So point P in the diagram is equal to (r cos(t), r sin(t))


We can see that as r increases, the diameter of the circle increases. As r approaches 0, the diameter of the circle decreases.


So when we use different values for each of the parametric equations, it seems that an ellipse is formed.

For further exploration graph , for different values of a and b and observe what happens.


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