Assignment 10

A parametric curve in the plane is a pair of functions

Look at the graph of

x = cos (at)

y = sin (bt)

When a=b, this graph will always be a circle with radius 1.

What happens when a and b are different values? For fun, let a = 3 and let b = -2.

If you would like to explore the graph of this equation when a and b are different values, click here!

Let's now look at the graph of

x = a cos(t)

y = b sin (t)

y = b sin (t)

Let a=b and explore different values of a=b.

As you can see from the graph, we get a set of concentric circles. The radius of each circle is determined by the value of a=b.

Now let's explore what happens when a does not equal b.

For the red ellipse below, a=3 and b=1.

For the purple ellipse below, b=1 and a=3.

Notice that when a > b, the
ellipse is stretched in the x direction. When b > a, the
ellipse is stretched in the y direction.

Click here to try your own values of a and b!

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Click here to try your own values of a and b!

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