How do you graph #xy = -8#?

1 Answer
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.


This rectangular hyperbola can be obtained by rotating the

rectangular hyperbola #xy = 8# about the origin through a right


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)#. .