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Math Help - Help checking whether this is right

  1. #1
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    Help checking whether this is right

    Hi,

    I am currently trying to find the area of segment of an elipse, I know the area of the segment for the circle related to the elleipse. So all i need to do is times the area of the circle segment by (b/a).

    The problem I have is that I don't know b. Am i right in thinking that if I know some points on the ellipse that I can rearange the forumal of ellipse to this:

    \frac{-\frac{x^{2}}{a^{2}}+1}{y^{2}}=b^{2}

    Sorry its all so long winded
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  2. #2
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    Quote Originally Posted by dan03uk View Post
    Hi,

    I am currently trying to find the area of segment of an elipse, I know the area of the segment for the circle related to the elleipse. So all i need to do is times the area of the circle segment by (b/a).

    The problem I have is that I don't know b. Am i right in thinking that if I know some points on the ellipse that I can rearange the forumal of ellipse to this:

    \frac{-\frac{x^{2}}{a^{2}}+1}{y^{2}}=b^{2}......No
    Sorry its all so long winded
    Unfortunately you calculated \dfrac1{b^2}

    If the center of the ellipse is at the origin the equation of the ellipse is

    \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1~\implies~\dfra  c{y^2}{b^2}=1 - \dfrac{x^2}{a^2} = \dfrac{a^2-x^2}{a^2}

    Now calculate the reciprocals on both sides of the equation:

    \dfrac{b^2}{y^2}=\dfrac{a^2}{a^2-x^2}~\implies~\boxed{b^2=\dfrac{a^2 y^2}{a^2-x^2}}
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