Question

Help with hyperbolas

Answer 1

Find the equation of the following hyperbola based on the following information: Vertices: (4,1), (4, 9), foci: (4, 0), (4, 10).

Answer 2

The center is at (4,0) i believe

Answer 3

so I believe our a = 1?

Answer 4

so then with that we can use our foci 10 to do 10^2=sqrt1^2 - b^2

Answer 5

@Nnesha does this look right so far?

Answer 6

The shifted hyperbola has the form \(\dfrac{(y -k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1\)
with center (h,k), vertices (h, k+b), (h, k-b)

Answer 7

Your vertices are (4, 1) and (4,9)
hence h =4,
k+b =1
k-b= 9
from them , we get k =5, b=-4

Answer 8

and \(c^2 = a^2+b^2\) hence a =3

Answer 9

since foci (4,0), (4,10) gives us the length of foci is 10 and c =5

Answer 10

I am so lost T_T

Answer 11

Combine all
\(\dfrac{(y-5)^2}{16}-\dfrac{x-4)^2}{9}=1\) is the required equation

Answer 12

Lost??? hehehe where?

Answer 13

I can see how h = 4

Ohhh ok
k-b=9
k+b = 1 thats how you ok ok I get that now

Answer 14

how did you get k= 5 and b=-4 so quickly?

Answer 15

add them together, you have 2k =10 , hence k =5

Answer 16

replace to any of them, you get b =-4

Answer 17

ohh ok that makes sense

Answer 18

any question? I have to go in 3 minutes. if you don't have any question. I log off now

Answer 19

I believe that is all

Answer 20

Thank you

Answer 21

ok