we notice the x of the foci don't change that means the hyperbola opens up and down [tex] \frac{(y-k)^2}{a^2}- \frac{(x-h)^2}{b^2}=1 [/tex] hmm center is (1,2) and vertices (1,5) and (1,-1) the distance to a vertex is 3, that is 'a' the rectangle of refernce is 6 units high remember that a²+b²=c² where a is major axis, b is minor axis and c is the distance from focs to center from focus to center is 5 units a is 3 3²+b²=5² 9+b²=25 mnus 9 b²=16 sqrt b=4
so [tex] \frac{(y-2)^2}{3^2}- \frac{(x-1)^2}{4^2}=1 [/tex] is the equation
