# 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 area cartesian equation chord circle combinations complex polygon cosh cosine cosine rule cube decagon derivative diagonal directrix dodecagon ellipse equilateral triangle exponent exponential exterior angle focus gradient hendecagon heptagon hexagon horizontal hyperbola hyperbolic function interior angle inverse hyperbolic function irregular polygon isosceles trapezium isosceles triangle kite locus major axis minor axis newton raphson method nonagon normal octagon parabola parallelogram parametric equation pentagon perimeter permutations power pythagoras proof quadrilateral radius rectangle regular polygon rhombus root sine sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs symmetry tangent tanh transformations trapezium triangle vertical