Geo5.2.7

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Find the equation of the ellipse in the usual form,if it passes thro'the points (-2,2) and (3,1).(axis are along the coordinate axes and centre at the origin).

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

It passes thro'(-2,2)\,,hence

4a^{2}+4b^{2}=a^{2}b^{2}\, equation 1

Also the ellipse passes thro' (3,1)\,

a^{2}+9b^{2}=a^{2}b^{2}\, equation 2.

Solving the two equations,

-32b^{2}=-3a^{2}b^{2},a^{2}={\frac  {32}{3}}\,

32a^{2}=5a^{2}b^{2},b^{2}={\frac  {32}{5}}\,

Hence,the equation of the ellipse is

3x^{2}+5y^{2}=32\,


Main Page:Geometry:The Ellipse