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!!!