# How do you graph xy = -8?

Aug 25, 2016

The graph is a rectangular hyperbola, with the two branches in Q2 and Q4. The asymptotes of the hyperbola are the axes of coordinates.

#### Explanation:

This rectangular hyperbola can be obtained by rotating the

rectangular hyperbola $x y = 8$ about the origin through a right

angle.

In Q2 and Q4, xy < 0. So the branches of the given

rectangular hyperbola lie in Q2 and Q4,

The asymptotes are x = 0 and y =0, so that,

when $x \to 0 , y \to \pm \infty$ and when $y \to 0 , x \to \pm \infty$.

The points that are closest to the center C at the origin are the

vertices $V \left(2 \sqrt{2} , - 2 \sqrt{2}\right) \mathmr{and} V ' \left(- 2 \sqrt{2} , 2 \sqrt{2}\right)$.

The eccentricity e = sqrt 2, for a rectangular hyperbola.

The transverse axis length 2a = 8.

The foci are at $S \left(4 , - 4\right) \mathmr{and} S ' \left(- 4 , 4\right)$. .