Question

How do u do question 6. Pls help fast

Answer 1

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

$4= \frac{a}{5-4} + 2 \\ \\ 2= \frac{a}{1} \\ \\ a=2 \\ \\ So,\ hyperbola\ has\ formula \\ \\ y= \frac{2}{x-4} +2$