Geo5.3.43

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Find the asymptotes of the hyperbola 2x^{2}+5xy+2y^{2}-11x-7y-4=0\,

The equation of the asymptotes is of the form 2x^{2}+5xy+2y^{2}-11x-7y+\lambda =0\,

2x^{2}+4xy+xy+2y^{2}-11x-7y+\lambda =0\,

(x+2y)(2x+y)+\lambda -11x-7y=0\,

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

2l+m=-11,l+2m=-7,lm=\lambda \,

l=-5,m=1\,

Hence the asymptotes are x+2y-5=0,2x+y+1=0\,


Main Page:Geometry:Hyperbola