# Geo5.3.35

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Find the equation of the hyperbola whose asymptotes are $7x+5y-3=0,2x+4y+1=0\,$ and passing thro' $(-2,1)\,$


Given asymptotes are $7x+5y-3=0,2x+4y+1=0\,$

The equation of the parabola is $(7x+5y-3)(2x+4y+1)+\lambda=0\,$

Given that the hyperbola passes through $(-2,1)\,$

$(-14+5-3)(-4+4+1)+\lambda=0,\lambda=12\,$

Therefore the equation of the hyperbola is $(7x+5y-3)(2x+4y+1)+12=0\,$

$14x^2+28xy+7x+10xy+20y^2+5y-6x-12y-3+12=0\,$

$14x^2+38xy+20y^2+x-7y+9=0\,$

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