Geo5.2.45

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Find the equation of the ellipse whose vertices are (-4,3),(8,3)\, and whose eccentricity is 5/6.

Given vertices (-4,3),(8,3),e={\frac  {5}{6}}\,

Since the ordinates of the two vertices are equal,the major axis is parallel to x-axis.

Therefore,major axis is 2a=8-(-4)=12,a=6\,

Now b^{2}=a^{2}(1-e^{2}),b^{2}=36(1-{\frac  {25}{36}})=11\,

Centre=mid point of the two vertices= \left({\frac  {8-4}{2}},{\frac  {3+3}{2}}\right)\,

Centre of the ellipse is (2,3).

The equation of the ellipse is {\frac  {(x-2)^{2}}{36}}+{\frac  {(y-3)^{2}}{11}}=1\,


Main Page:Geometry:The Ellipse