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# 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