Question

How do I write the equation of hyperbola in standard form with center (0,0),endpoints of the transverse axis (±6,0) and length of latus rectum is 16?

Answer 1

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