Geo5.3.5

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Determine the equation to the hyperbola whose centre is (0,0),distance between the foci is 18 and that between the directrices is 8.

Given 2ae=18,{\frac  {2a}{e}}=8\,

ae=9,{\frac  {a}{e}}=4\,

a^{2}=9(4),a=6,e^{2}={\frac  {9}{4}}\,

b^{2}=a^{2}(e^{2}-1),b^{2}=36({\frac  {9}{4}}-1)=45\,

Therefore,the equation of hyperbola is {\frac  {x^{2}}{36}}-{\frac  {y^{2}}{45}}=1\,


Main Page:Geometry:Hyperbola