How do you find the equations of the asymptotes of this hyperbola?

-x^2 + y^2 + 6x - 16y - 9 = 0

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- May 30th 2009, 09:36 AMjumpman23Asymptotes of a Hyperbola
How do you find the equations of the asymptotes of this hyperbola?

-x^2 + y^2 + 6x - 16y - 9 = 0 - May 30th 2009, 11:55 AMearboth
- May 31st 2009, 08:25 AMHallsofIvy
Here's another way of arguing. The "asymptotes" of a hyperbola are the lines the hyperbola approaches for

**very very**large values of x and y.

The equation of the hyperbola is as Earboth said. For**very very**large x and y those squares will each be far larger! Large enough that that "1" on the right side is negligible compared to them: For**very very**large x and y, that equation is very very close to from which we get and then . Taking x- 3= y- 8, y= x+ 5. Taking x- 3= -(y- 8), x- 3= -y+ 8, y= -x+ 11, the answer that Earboth gave.