# Rectangular hyperbola example

Categories: coordinate systems pure mathematics

A rectangular hyperbola has the parametric equations:

$$ \begin{align} x = c t\newline y = \frac{c}{t} \end{align} $$

Where $c$ is a positive constant, and $t$ is the independent variable.

We can plot this curve by calculating the values of $x$ and $y$ for various values of $t$, and drawing a smooth curve through them.

## Curve for c = 1

Assuming $a = 1$, the parametric equations simplify to:

$$ \begin{align} x = t\newline y = \frac{1}{t} \end{align} $$

The values are shown in the following table, for $t$ in the range -3 to +3:

t | x | y |
---|---|---|

-4 | -3 | -0.25 |

-2 | -2 | -0.5 |

-1 | -2 | -1 |

-0.5 | -0.5 | -2 |

0 | 0 | undefined |

0.5 | 0.5 | 2 |

1 | 1 | 1 |

2 | 2 | 0.5 |

4 | 4 | 0.25 |

Here are the points plotted on a graph:

This curve is actually a standard *reciprocal curve*, as shown here.

The curve can be drawn by plotting the points and drawing a smooth line through them. Notice that the curve value is undefined for $t = 0$:

## See also

## Join the GraphicMaths Newletter

Sign up using this form to receive an email when new content is added:

## Popular tags

angle cartesian equation chord circle combinations cosh cosine cosine rule cube diagonal directrix ellipse equilateral triangle exponential exterior angle focus horizontal hyperbola hyperbolic function interior angle inverse hyperbolic function isosceles triangle locus major axis minor axis normal parabola parametric equation permutations power quadrilateral radius root sine rule sinh sloping lines solving equations solving triangles square standard curves straight line graphs tangent tanh transformations triangle vertical