Geo5.2.9

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Find the eccentricity of the ellipse ,if its length of the latus rectum is equal to half of its major axis.

Let the equation be {\frac  {x^{2}}{a^{2}}}+{\frac  {y^{2}}{b^{2}}}=1\,

Given that,the length of the latus rectum=1/2 major axis

i.e {\frac  {2b^{2}}{a}}={\frac  {1}{2}}(2a)\,

2b^{2}=a^{2}\,

Therefore 2a^{2}(1-e^{2})=a^{2},1-e^{2}={\frac  {1}{2}},e={\frac  {1}{{\sqrt  {2}}}}\,


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