Geo5.3.4

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Obtain the equation of the hyperbola in standard form whose latusrectum is 4 and eccentricity is 3.

Given {\frac  {2b^{2}}{a}}=4,e=3\,

b^{2}=2a\,

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

a={\frac  {1}{4}}\,

b^{2}={\frac  {1}{2}}\,

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


Main Page:Geometry:Hyperbola