Geo5.2.6

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If the two ends of major axis of an ellipse are (5,0),(-5,0).Find the equation of ellipse if its focus lies on the line 3x-5y-9=0\,

The distance between the two ends is {\sqrt  {100}}=10\,

Now

2a=10,a=5\,

Let the focus be (ae,0)

3ae-5(0)-9=0,ae=3,e={\frac  {3}{5}}\,

e^{2}={\frac  {25-b^{2}}{25}}\,

9=25-b^{2},b=4\,

Now the equation of the ellipse is {\frac  {x^{2}}{25}}+{\frac  {y^{2}}{16}}=1\,

16x^{2}+25y^{2}=400\,

Main Page:Geometry:The Ellipse