Geo5.2.44

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Find the equation of the ellipse whose vertices are (-4,1),(6,1)\, and whose focus lies on the line x-2y=2\,

Given vertices (-4,1),(6,1)\,

The distance between the vertices is 10=2a,a=5\,

Therefore centre= \left({\frac  {-4+6}{2}},{\frac  {1+1}{2}}\right)\,

Equation to the major axis is y-1=0\,

Focus lies on the line x-2y=2\,

Solving these two equations, we get the point as (4,1).

The distance from the centre to the focus is ae=3

Hencea^{2}e^{2}=a^{2}-b^{2},b^{2}=16\,

Hence the equation of ellipse is {\frac  {(x-1)^{2}}{25}}+{\frac  {(y-1)^{2}}{16}}=1\,


Main Page:Geometry:The Ellipse