Answer:
Length of latusrectum =9=
a
2b
2
⇒b
2
=
2
9a
..... (i)
and e=
4
5
∵1+
a
2
b
2
=
16
25
∴1+
2a
2
9a
=
16
25
[from Eq. (i)]
⇒
2a
9
=
16
9
⇒a=8
On putting the value of a in Eq. (i), we get
b
2
=
2
9×8
=36⇒b=6
∴ Equation of hyperbola is
8
2
x
2
−
6
2
y
2
=1⇒
64
x
2
−
36
y
2
=1
