The general form for a hyperbola with the center at the origin and a vertical transverse axis is:
y2/a2 - x2/b2 = 1
From the given:
a = 12
To get b, we use the given distance between the foci.Since it's 26,
c = 26/2 = 13
Using this defintion:
c2 = a2 + b2
b = sqrt(c2 - a2) = sqrt (13^2 - 12^2) = 5
The equation therefore is:
y2/13^2 - x2/5^2 = 1
or
y2/169 - x2/25 = 1
