Assignment 10

Parametric Curves

Charles Meyer

Parametric curves are an interesting investigation in to mathematics. This investigation will look at the affects of different values of variables on a parametric equation with sine and cosine. The parametric equation I will look at in this investigation is shown below

To begin my investigation, I will set my variables a & b to the value of 1. My t will consist of a range from 0 to 2Pi. The initial investigation gives the graph of a circle with a radius of 1.


I now need to take the investigation a bit further and see how change the value of the a and/or b variable changes the shape and size of the figure. I begin by changing the variable a while keeping by variable b as a constant.

a = 2, b = 1a = 3, b = 1

As expected, changes with the a variable changes the curve along the x-axis. I will now verify if the same thing would occur on the y-axis if I changed the b variable.

b = 2, a = 1 b = 3, a = 1

Once again, the curves change along the y-axis when the b variable is change.


But what do the values of a & b really mean in terms of our circles/ovals? Well, through the investigation we see that the values assigned to a & b are actually the intercept of the x & y axis respectfully as the value of t moves along its range. Further investigation shows the larger the difference between the two variables the leaner, more narrow the oval becomes. Two examples are shown below.

a = 0.25, b = 3a = 3, b = 0.25