Geo5.3.44

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Find the asymptotes of the hyperbola 2x^{2}-xy-y^{2}+2x-2y+2=0\,

The equation of the asymptotes of the given hyperbola is of the form

ax^{2}-xy-y^{2}+2x-2y_{\lambda }=0\,

(2x+y)(x-y)+2x-2y+\lambda =0\,

Let the equation be (2x+y+l)(x-y+m)=0\,

l+2m=2,-l+m=-2\,

Solving,we get

l=2,m=0\,

The asymptotes are

2x+y+2=0,x-y=0\,


Main Page:Geometry:Hyperbola