Question

How do you graph `xy = -8`?

Answer 1

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 `xy = 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 +-oo` and when `y to 0, x to +-oo`.

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

vertices `V(2 sqrt 2,-2 sqrt 2) and V'(- 2 sqrt 2, 2 sqrt 2)`.

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

The transverse axis length 2a = 8.

The foci are at `S(4, -4) and S'(-4, 4)`. .