Geo5.3.3

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What is the equation to the hyperbola if the latusrectum is 9/2 and eccentricity is 5/4.

Given that{\frac  {2b^{2}}{a}}={\frac  {9}{2}},e={\frac  {5}{4}}\,

b^{2}=a^{2}(e^{2}-1),b^{2}={\frac  {9a}{2}}\,

{\frac  {9a}{4}}=a^{2}({\frac  {25}{16}}-1)\,

{\frac  {9}{4}}=a({\frac  {9}{16}}\,

a=4\,

b^{2}=9\,

Therefore,the equation of hyperbola is {\frac  {x^{2}}{16}}-{\frac  {y^{2}}{9}}=1\,


Main Page:Geometry:Hyperbola