Geo5.3.36

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Find the equation of the hyperbola whose asymptotes are 2x+3y-5=0,5x+3y-8=0\, and passing thro' (1,-1)\,

Given asymptotes are 2x+3y-5=0,5x+3y-8=0\,

The equation of the hyperbola is (2x+3y-5)(5x+3y-8)+\lambda =0\,

The hyperbola passes through (1,-1)\,

(2-3-5)(5-3-8)+\lambda =0\,

\lambda =-36\,

Hence the equation of hyperbola is (2x+3y-5)(5x+3y-8)-36=0\,

10x^{2}+6xy-16x+9y^{2}+15xy-24y-25x-15y+40-36=0\,

10x^{2}+21xy+9y^{2}-41x-39y+4=0\,


Main Page:Geometry:Hyperbola