# ParametricPlot doesn't give what I expected

**URL:** <https://community.wolfram.com/t/parametricplot-doesnt-give-what-i-expected/18019>\
**Category:** Questions\
**Tags:** calculus, graphics-and-visualization\
**Created:** [April 25, 2021, 10:02pm UTC](https://community.wolfram.com/t/parametricplot-doesnt-give-what-i-expected/18019 "2021-04-25T22:02:44Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![janiskoehler](https://avatars.discourse-cdn.com/v4/letter/j/53a042/32.png) [@janiskoehler](https://community.wolfram.com/u/janiskoehler)\
**Post date:** [April 25, 2021, 10:02pm UTC](https://community.wolfram.com/t/parametricplot-doesnt-give-what-i-expected/18019/1 "2021-04-25T22:02:44Z")

</div>

Hey guys, here’s a very simple code I wrote, it’s basically just one line. But I don’t understand what is going on at all. I tried to parametrize two functions and to plot the result as a parametric plot. But the plot itself shows 2 lines? Does anyone see what is going on here? Upon changing the lower and upper bounds for u the behavior changes and I’m simply very confused.

Code:

```
ParametricPlot[{2*u^3/(u^2 - 1), 2*u^3/(1 + u^2)^2}, {u, 1.01, 5}, 
PlotRange -> All]

```

Thanks in advance!

J.D.

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<div class="post-metadata">

**Author:** ![neils](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/neils/32/20595_2.png) [@neils](https://community.wolfram.com/u/neils)\
**Post date:** [April 25, 2021, 10:27pm UTC](https://community.wolfram.com/t/parametricplot-doesnt-give-what-i-expected/18019/2 "2021-04-25T22:27:01Z")

</div>

Janis,

You need to also set the AspectRatio because the plot has a very small y values with huge x values.

```
ParametricPlot[{2 u^3/(u^2 - 1), 2 u^3/(1 + u^2)^2}, {u, 1.01, 5.}, 
 AspectRatio -> 0.5, PlotRange -> All]

```

The plot looks like two curves but it is actually the same curve if you look at the data. The manual way to see it is

```
ListLinePlot[
 Table[{2 u^3/(u^2 - 1), 2 u^3/(1 + u^2)^2}, {u, 1.01, 5, .01}], 
 PlotRange -> All]

```

Both give you

 ![ScreenShot2021-04-25at6.23.18PM.png](https://global.discourse-cdn.com/wolfram/original/2X/f/fb50b26c0ed92f3d8b10073a09cca8acb72e54d5.png)

If you look at the terms, this makes sense:

```
Plot[{2 u^3/(u^2 - 1), 2 u^3/(1 + u^2)^2}, {u, 1.01, 5}]

```

The x curve goes to a minimum and then rises again so the parametric plot will have an inflection point.

Regards,

Neil

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<div class="post-metadata">

**Author:** ![janiskoehler](https://avatars.discourse-cdn.com/v4/letter/j/53a042/32.png) [@janiskoehler](https://community.wolfram.com/u/janiskoehler)\
**Post date:** [April 26, 2021, 4:45am UTC](https://community.wolfram.com/t/parametricplot-doesnt-give-what-i-expected/18019/3 "2021-04-26T04:45:16Z")

</div>

Thank you, that helps a lot.

J.D.