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Math Help - Finding the equation of an ellipse

  1. #1
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    Finding the equation of an ellipse

    I need help with expanding the equation of a central ellipse. I know that

    PF1+PF2 = sum of focal radii

    sqrt[(x-0)^2+(y+3)^2] + sqrt[(x-0)^2+(y-3)^2] = 10

    How do I get rid of the radicals?
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  2. #2
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    Quote Originally Posted by sun95 View Post
    I need help with expanding the equation of a central ellipse. I know that

    PF1+PF2 = sum of focal radii

    sqrt[(x-0)^2+(y+3)^2] + sqrt[(x-0)^2+(y-3)^2] = 10

    How do I get rid of the radicals?
    Move a radical to the right hand side. Square both sides. Simplify. Isolate the remaining radical. Square both sides again. Simplify. Finito.
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  3. #3
    Member rtblue's Avatar
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    \displaystyle\sqrt{x^2+(y+3)^2}+\sqrt{x^2+(y-3)^2}=10

    square both sides.

    \displaystyle x^2+(y+3)^2+x^2+(y-3)^2+2\sqrt{[x^2+(y+3)^2][x^2+(y-3)^2]}=100

    \displaystyle 2x^2+2y^2-82=-2\sqrt{[x^2+(y+3)^2][x^2+(y-3)^2]}

    \displaystyle 4x^4+4y^4+8x^2y^2-328x^2-328y^2+6724=4[x^4+y^4+2x^2y^2+18x^2-18y^2+81]

    Notice many of the terms will cancel out upon further simplification. I'll leave you to do the rest.
    Last edited by rtblue; January 8th 2011 at 04:56 PM. Reason: Further Simplification
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