Question

What are the asymptotes of the hyperbola below?

Answer 1

@pgpilot326 Can you help me plz?

Answer 2

did you make the box?

Answer 3

no

Answer 4

here's a link you can check out and refernece but i'll help you through this one real quick.

http://www.purplemath.com/modules/hyperbola.htm

first, you want to get it in the right form:
\[\frac{ (x-h)^2 }{ a^2 }-\frac{ (y-k)^2 }{ b^2 }=1\]
yours is almost there, just have to rewrite the denominators:
\[\frac{ (x-13)^2 }{ 9^2 }-\frac{ (y+8)^2 }{ 3^2 }=1\]
the center of the hyperbola (and the box you're going to make is at the point (h, k) and in your case this is (13, -8).

from there we simply add and subtract a & b from the x & y, resp., to get the corners of the box.
(h+a, k+b), (h+a, k-b), (h-a, k+b), (h-a, k-b)

those are the locations of the corners of the box. the asymptotes of the hyperbola go through the box diagonally, right through the corners.



to find the equations for the lines that are the asymptotes, you can use 2 points, find the slope and then use one of those points in the point-slope form.

the link actually gives you a handy way to get the lines from a, b, h & k.