GraphicMaths

Visualising maths

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.