Find an equation for the hyperbola that has the vertices 0 4

Solution

Since the vertices are at (0, -4) and (0, 4), the center is at (0,(-4+4)/2) =(0, 0)
As 4 - 0 = 4, the hyperbola will be of the form
y²/4² - x²/c² = 1

Then, substituting, (-5, 6), we get

6²/4² - 5²/c² = 1

5²/c² = 6²/4² - 1 = 9/4 - 1 = 5/4

5²/c² =  5/4

Cross-multiplying,

5c² = 100

c² = 20

c = 25

Then, we may write this equation either as

y²/4² - x²/(25)² = 1, or

y²/16 - x²/20 = 1