Write an equation for the hyperbola that satisfies the given set of conditions. vertices (16,0) and (-16,0) conjugate axis of length 16 units.

  vertices (23 , 0) and (-23 , 0) ==> 
center (0 , 0), a = 23 
if conjugate axis = 6 = 2b, then b = 3 

for hyperbola that opens L and R (as shown by the vertices): 
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 , where (h,k) is the center 

x^2 / 23^2 - y^2 / 9 = 1 
(center (0,0)) 

2nd one is similar 
(center (0,0), a = 18 , b = 7) 

3rd: standard form for hyperbola that opens up and down: 
(y - k)^2 / a^2 + (x - h)^2 / b^2 = 1 

a = 17, b = 5, (h,k) = (0,0) 
center is always halfway between the vertices 
y^2 / 17^2 - x^2 / 5^2 = 1 

4th is similar to 3rd, 
center (0,0) , a = 16 , b = 7 

b = half of the conjugate axis

Hope it helps!!!