Rectangular hyperbola example

By Martin McBride, 2020-09-12
Tags: parametric equation hyperbola
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

adjacency matrix alu and gate angle area argand diagram binary maths cartesian equation chain rule chord circle cofactor combinations complex polygon complex power complex root cosh cosine cosine rule cpu cube decagon demorgans law derivative determinant diagonal directrix dodecagon ellipse equilateral triangle eulers formula exponent exponential exterior angle first principles flip-flop focus gabriels horn gradient graph hendecagon heptagon hexagon horizontal hyperbola hyperbolic function infinity integration by substitution interior angle inverse hyperbolic function inverse matrix irregular polygon isosceles trapezium isosceles triangle kite koch curve l system locus maclaurin series major axis matrix matrix algebra minor axis nand gate newton raphson method nonagon nor gate normal not gate octagon or gate parabola parallelogram parametric equation pentagon perimeter permutations polar coordinates polynomial power product rule pythagoras proof quadrilateral radians radius rectangle regular polygon rhombus root set set-reset flip-flop sine sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs surface of revolution symmetry tangent tanh transformations trapezium triangle turtle graphics vertical volume of revolution xnor gate xor gate