[tex]y= \frac{a}{x-h} +k
\\x=4 \ vertical\ asymptote
\\ Vertical\ asymptote \ can\ be\ found \ from
\\ \\x - h = 0,\ x=h,
\\ \\ so \ h = 4
\\ \\ y= \frac{a}{x-4} + k= \frac{a+kx-4k}{x-4}
\\Vertical\ asymptote \ can\ be\ found\ as
\\ \\ \frac{kx}{x} = k.
\\ We\ know\ that\ vertical\ asymptote\ is\ 2,\ so\ k=2.
\\ \\ y= \frac{a}{x-4} + 2
\\ \\ We \ need\ to\ find\ a.\ We\ have\ point\ (5,4),\ that\ belongs\ to\ \\this\ function.\ So,
\\ \\ y= \frac{a}{x-4} + 2
\\ \\4= \frac{a}{5-4} + 2
[/tex]
[tex]4= \frac{a}{5-4} + 2
\\ \\ 2= \frac{a}{1}
\\ \\ a=2
\\ \\ So,\ hyperbola\ has\ formula
\\ \\ y= \frac{2}{x-4} +2[/tex]
