What is the equation of the hyperbola with vertices at (0,-4) and (0,4) and foci at (0,-6) and (0,6)?

Step-by-step explanation:

We are given equation of hyperbola

Vertices are (0,-4) (0,4)

we can use formula

vertices :  (h , k+a) and (h,k-a)

we can compare and find h , k and 'a'

we can add both equations

we get

now, we can find 'a'

now, we can use foci formula

foci: (h, k + c), (h, k - c)

we know that

so, we can solve for b

now, we can use standard equation of hyperbola

now, we can plug values

Step-by-step explanation:

Given the two co-ordinates:

A(x1,y1) = (-4,-8)

B(x2,y2) = (-4,0)

Putting them in the distance formula:

Hope this helped!