A **parametric equations grapher** is a *grapher* that draws the range of a function p(t) = **[f(t), g(t)]** on a given *domain* in a coordinate system. Such a graph is called the graph of the parametric equations ** x = f(t)** &

**or the**

*y*= g(t)**parametric curve**

*represented*by the function

**p(t)**.

Utilizing the most sophisticated coordinate systems, this **parametric equations grapher** uses **animation** to graph **parametric curves**.

The animated graph shows how **parametric curves** are constructed not just in the **Cartesian** but also in the **polar coordinate system** — actually, it's the only known grapher that is even capable of graphing **parametric curves** in the **polar coordinate system**.

You can start **animation** by pressing ► at the bottom of the graphing area (if it's hidden, press the **Animate** button first).

It starts the animation of the **parametric graphing process** of the **parametric expression** ** in focus**. The graph is drawn

*progressively*from the initial value to the final value of t.

You can then press **||** to *pause* the **animation** or press **Done** to *stop* it. This also closes the **animation** interface. To display it again press the **Animate** button at the top of the parametric grapher.

You can also change the **speed of ** **parametric graphing animation** by using the **slider** provided

In addition, it's also the only **parametric curve grapher** that enables you to rotate any of the coordinate axes and thus graph parametric curves in **non-orthogonal** Cartesian coordinate systems.

**pi**is replaced by**π**.**inf**(**infinity**) is replaced by**2π**.

*You can use your mouse to Rotate Axis, Translate and Change Scale*

In addition to inputting data — by first pressing the *gear* button — you can use your mouse to perform some functionality unique to this **interactive parametric grapher** as outlined below.

- Click on (or near) an axis and move your mouse. That will
**rotate the axis**. The graph(s) are re-drawn in the**non-orthogonal**(*non-perpendicular*) Cartesian coordinate system. Click again to release the axis. - Drag the mouse to
**move the coordinate system**together with the graphs. - Double-click in the canvas to
**move the origin**to where was clicked. - Hold down Alt key and click on an axis to
**change the scale (zoom in one direction)**; the point which was clicked will be labelled "1" (or "-1") and becomes the new unit for that axis.

**Lines**

**Circles**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Other parametric graphs**

**Butterfly curve**

**Lines**

**Circles**

**Spirals**

**Roses**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Cardioids**

**Limacons**

**Lemniscates**

**Other parametric graphs**

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To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the pop-up menu.