Given: The hyperbola is centred at origin i.e O (0, 0), length of transverse axis is 6 and one focus is (0, 4). ∵ The foci of the given hyperbola are of the form (0, ± c), it is a vertical hyperbola i.e it is of the form:
y2
a2
−
x2
b2
=1 ⇒c=4 and c2=16 As we know that, the length of tranverse axis of the hyperbola of the form
y2
a2
−
x2
b2
=1 is given by: 2a ⇒2a=6 ⇒a=3 and a2=9 As we know that b2=c2−a2 ⇒b2=16−9=7 Hence, the equation of required hyperbola is: