HYPERBOLA TRANSFORMATION
FIRST STEP:
a) set two slides called a and b
b) insert the standard equation of the hyperbola
c) insert the equations of the asymptotes y=+bx/a and y=-bx/a
d) as you can see you got the graph of an "standard hyperbola" 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.
SECOND STEP
a) set each a and b to the value of one, you'll get an "equilateral hyperbola" referred to the axes (that means both Foci are on the axes);
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 "reciprocal function" referred to the asymptotes (that means both Foci are now on the bisectors);
LAST STEP
a) Create a vector V(4;2);
b) now give the graph a translation of vector V and you'll get the "homographic function" referred to the asymptotes.