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Find the equation to the hyperbola whose asymptotes are 3x=\pm 5y\, and vertices are (\pm 5,0)\,

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

Combined equation of asymptotes is (3x-5y)(3x+5y)=0,9x^{2}-25y^{2}=0\,

Therefore equation of the hyperbola is 9x^{2}-25y^{2}=k\,

Vertices (\pm 5,0)\, lie on the hyperbola, hence 9(25)=k,k=225\,

Therefore,equation of the hyperbola is 9x^{2}-25y^{2}=225,{\frac  {x^{2}}{25}}-{\frac  {y^{2}}{9}}=1\,

Main Page:Geometry:Hyperbola