How do you find the asymptotes of a hyperbola?

[Chadlee88]

How do u find the asymptotes to hyperbolas??

what are the asymptotes to this equation?

-x^2/4 + y^2/8 = 1

i really need help

 

[HallsofIvy]

Suppose x and y are very, very large. Then that "1" on the right hand side of
-\frac{x^2}{4}+ \frac{y^2}{8}= 1
is very very small compared to the other two terms so the equation is approximately
-\frac{x^2}{4}+ \frac{y^2}{8}= 0

Of course, -\frac{x^2}{4}+ \frac{y^2}{8}
factors as
(\frac{x}{2}+ \frac{y}{\sqrt{8}})(-\frac{x}{2}+\frac{y}{\sqrt{8}})
so for large x,y your equation is approximately
(\frac{x}{2}+\frac{y}{2\sqrt{2}})(-\frac{x}{2}+\frac{y}{2\sqrt{2}})= 0

Certainly if "ab= 0" then either a= 0 or b= 0. That gives you two linear equations whose graphs are close to the hyperbola for large x,y: the asymptotes.