Since the coordinates of the one focus at (0, 4) = (0 , ±c ), it is a case of vertical hyperbola ⇒ c = 2 It is a case of vertical hyperbola ⇒ The equation of hyperbola is
y2
b2
−
x2
a2
=1 .......(1) Length of the transverse axis = 6 ⇒2a=6 ⇒a=3 Also c2=a2+b2 ⇒22=32+b2 ⇒b2=7 Equation (1) becomes
y2
9
−
x7
7
=1 Hence, The equation of the hyperbola with center at the origin, length of the transverse axis is 6 and one focus at (0, 4) is