## Parametric equation of ellipse

The Parametric equation of an ellipse is:

```
$$
x = a \cos{t}\\
y = b \sin{t}
$$
```

## Understanding the equations

We know that the equations for a point on the unit circle is:

```
$$
x = \cos{t}\\
y = \sin{t}
$$
```

Multiplying the `$x$`

formula by `$a$`

stretches the shape in the x direction, so that is the required width (crossing the x axis at `$x=\pm a$`

:

Multiplying the `$y$`

formula by `$b$`

stretches the shape in the y direction, so that is the required height (crossing the y axis at `$x=\pm b$`

.
This creates the required ellipse shown at the top of this article.