# Comparing parametric equations

1. Nov 6, 2013

### Jbreezy

1. The problem statement, all variables and given/known data

Compare the curves represented by the the parametric equations. How do they differ?
a.) x =t , y = t^-2
b.) x = cost , y = (sect)^2
c.) x = e^t , y = e^(-2t)

2. Relevant equations
So I drew them on the calculator they all look like umm... how do I describe this picture the x and y axis ...now picture ...well just picture 1/x^2 that is what they kind look like.

3. The attempt at a solution

I'm just having issue coming up with a reasonable explanation. I'm not sure they all pretty much look the same. . Maybe I can say that the rate at which T changes ? So for equation a.) with one change in t you get one change in x and in y you get smaller and smaller changes in it as t increases. Which is slower then say equation b? I don't know

2. Nov 6, 2013

### Staff: Mentor

Think about the point on each graph that corresponds to various values of t, say t = 0. Also think about the orientation. As t increases, which direction does a point move along the curve?

3. Nov 6, 2013

### pasmith

Note that in (b) you have $-1 \leq x(t) \leq 1$ (and there's a problem with y when $x(t) = 0$), but in (a) and (c) $x \geq 0$.

4. Nov 6, 2013

### Jbreezy

How does a an c differ also? Thanks for response

5. Nov 6, 2013

### Staff: Mentor

What's the difference in the graphs of x = t vs. x = et, aside from the obvious difference in the shapes?

6. Nov 6, 2013

### Jbreezy

Hmm. Well lol one is exponential? I don't know. x = e^t goes faster?

7. Nov 6, 2013

### Staff: Mentor

Are the domains the same?

8. Nov 6, 2013

### Jbreezy

No well x = t is neg to pos inf. and x = e^t is but x will never be 0 here

9. Nov 6, 2013

### Staff: Mentor

Seems like that's an important difference between the graphs of a and c.

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