Answer the following questions about hyperbolas centred at the origin.
(i) Give the definition of a hyperbola in terms of a constant difference of distances from two fixed points.
(ii) Show, by naming the meaningful parameters, how the relation c2=a2+b2 arises for a hyperbola whose transverse axis lies on the x–axis.
(iii) Explain how the standard equation changes when the transverse axis is taken along the y–axis and write that standard form.