a) set two slides called a and b[br]b) insert the standard equation of the hyperbola [math]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/math][br]c) insert the equations of the asymptotes y=+bx/a and y=-bx/a[br]d) as you can see you got the graph of an "[b]standard hyperbola" [/b]referred to the axes (that means both Foci are on the axes) , if you change the values of both slides you can see how the hyperbola's graph change its graph.

a) set each a and b to the value of one, you'll get an "[b]equilateral hyperbola[/b]" [math]x^2-y^2=\pm1[/math] referred to the axes (that means both Foci are on the axes);[br]b) now as you can see in the next step if you give the graph a rotation of 45° centred on the origin of the axes, you'll get the "[b]reciprocal function" [/b] [math]y=\frac{1}{x}[/math] referred to the asymptotes (that means both Foci are now on the bisectors);[br]

a) Create a vector V(4;2);[br]b) now give the graph a translation of vector V and you'll get the "[b]homographic function[/b]" [math]y=\frac{ax+b}{cx+d}[/math] referred to the asymptotes.