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

468

step-by-step explanation:

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