Given equation of hyperbola is

x2

16

−

y2

9

= 1 which is of the form

x2

a2

−

y2

b2

= 1.
The foci and vertices of the hyperbola lie on x-axis.
Now, a2 = 16 ⇒ a = 4 and b2 = 9 ⇒ b = 3
Also, c2 = a2+b2 = 16 + 9 = 25 ⇒ c = 5
∴ Coordinates of foci are (± c, 0) i.e. (± 5, 0)
Coordinates of vertices are (± a, 0) i.e. (± 4, 0)
Eccentricity (e) =

c

a

=

5

4

Length of latus rectum =

2b2

a

=

2×9

4

=

9

2