Construct the graph of an hyperbola by its definition:
An hyperbola is the set of all points on a plane where the absolute value of the difference between the distances from two fixed points F1 and F2 is constant - I PF1-PF2 I=COST.
a) set a slider called c
b) draw a line passing trough a point C. Take on this line a point D and draw a segment DC (rename this segment PF2); of four units and take a point C on it;
c) draw a circumference centred in C and radius = PF2+c; name E the intersection point between the line and the circumference and set the segment CE calling it PF1;
d) on the x-axis plot down two points F1 and F2 having coordinates (-1,0) and (+1,0);
e) draw a circumference centred in F1 and radius PF1 and another one with radius PF2; do the same on F2.; then a circumference centred in F2 and radius CB; label P and G the intersection points between the two circumferences on both sides and then activate "traces"; connect P with the foci;
f) move D on the segment DE and you will get the graph of an hyperbola.