A **parametric equations grapher** is a *grapher* that draws the range of a function p(t) = **[f _{1}(t), ..., f_{n}(t)]** on a given

*domain*in a coordinate system. Such a graph is called the graph of the parametric equations

**, ...,**

*x*= f_{1}_{1}(t)**or the**

*x*= f_{n}_{n}(t)**parametric curve**

*represented*by the function

**p(t)**.

Utilizing the most sophisticated coordinate systems, this **Cartesian** and **polar parametric equations grapher** uses **animation** to graph **parametric curves** given by the **parametric equations** **x = f(t)** & **y = g(t)** or represented by the function p(t) = **[f(t), g(t)]**.

The **animated parametric curve** shows how the **Cartesian** and **polar** **graphs** of **parametric equations** are constructed progressively on their domain — it's the only known **polar parametric equations grapher** that is even capable of graphing **parametric curves** in the **polar coordinate system**.

The **parametric grapher** starts **animation** of the **parametric expression** *in focus* when you press ► at the bottom of the graphing area (if it's hidden, press the **Animate** button first).

The **parametric graph** is drawn *progressively* from the initial value to the final value of t to give you an insight into the process of the **parametric graphing**.

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**

Calculator is loading.

Please wait....

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.