Question

find the coordinates of the foci of the hyperbola y²-16x²=16.​

Answer 1

Step-by-step explanation:

We have, 16x

2

−9y

2

=576

⇒

36

x

2

−

64

y

2

=1

⇒

6

2

x

2

−

8

2

y

2

=1...(1)

On comparing equation (1) with the standard equation of hyperbola,

a

2

x

2

−

b

2

y

2

=1,

we obtain a=6,b=8⇒e=

1+

a

2

b

2

=

1+

36

64

=

3

5

Therefore, the coordinates of the foci are (±10,0)

The coordinates of the vertices are (±6,0)

Eccentricity e=

3

5

Length of latus rectum =

a

2b

2

=

6

2×64

=

3

64

Answer 2

Step-by-step explanation:

i cant answer this sorry best of luck