Find Standard Form of the equation of the hyperbola

Question

Find the standard form of the equation of the hyperbola with the given characteristics.

Vertices: (5, 1), (5, 15); foci: (5, 0), (5, 16)

So, I did this 3 times and Im going insane. The 5's are whats messing me up. Can anyone help?

 

 

Answer 1

The center is at (5,(1+15)/2) =(5,8)

The vertex is15-8 =7 from the center

The focus is 16 -8 = 8 from the center

Thus, to find b² in the equation of the hyperbola, we use b² = c² - a² = 8² - 7² =15.

Then, as 7² =49,

the equation of the hyperbola is (y-8)²/49 - (x-5)²/15 = 1