For each hyperbola described below: (1) derive an equation of the form
x2/a2 − y2/b2 = 1 or y2/b2 − x2/a2 = 1.
(2) state any x- or y-intercepts. (3) find the equations for the asymptotes of the hyperbola.
a. let the foci be a(−2,0) and b(2,0), and let p be a point for which either pf − pg = 2 or pg − pf = 2.
b. let the foci be a(−5,0) and b(5,0), and let p be a point for which either pf − pg = 5 or pg − pf = 5.
c. consider a(0, −3) and b(0,3), and let p be a point for which either pf− pg = 2.5 or pg − pf = 2.5.
d. consider a(0, −√2) and b(0, √2), and let p be a point for which either pf − pg = 2 or pg − pf = 2.