Now we will look at the cases when

a = b.

 

In this part of our investigation of parametric equations, we will be using the parametic equations

where 0 < t < 2Pi.

---

 

a = b

---

a = -b

---

-a = b

---

Conclusions:

Notice that even though we have changed the positive and negative values of each a and b, the graphs remain the same.

Each graph crosses the x-axis and the y-axis at a positive and negative a value and a positive and negative b value.

So instead of looking at the posasibilities when a = b, it may be more fitting to look at IaI = IbI.

 

What we can tell from the graphs, is that when evaluating the graphs of parametric equations

where IaI = IbI,

we have a succession of circles centered around the origin with the radii IaI = IbI.

 

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