Results 1 to 2 of 2

Math Help - Area of an ellipse

  1. #1
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1

    Area of an ellipse

    Just a quick query about calculating the area of an ellipse:

    We've given the following parametric coordinates of an ellipse C:

    x = a \cos{t} and y = b \sin{t} and asked to find the area enclosed.

    It's easy enough to find the following derivatives:

    \frac{dx}{dt}  = -a \sin{t} and \frac{dy}{dt}  = b \cos{t}

    But then in the answers it's stated that:

    The area of an ellipse is given by \frac{1}{2} \int_C x dy - y dx

    Just wondering have they worked this out, or is this a common formula?

    Thanks for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by craig View Post
    Just a quick query about calculating the area of an ellipse:
    Just wondering have they worked this out, or is this a common formula?
    It is a common formula deduced from the Green's Theorem:

    \dfrac{1}{2}\displaystyle\int_{C}xdy -ydx=\dfrac{1}{2}\displaystyle\iint_{D}\left(\frac{  {\partial Q}}{{\partial x}}-\frac{{\partial P}}{{\partial y}}\right)dxdy=\dfrac{1}{2}\displaystyle\iint_{D}(  1+1)dxdy=\displaystyle\iint_{D}dxdy=A

    and A is the area of D .

    Regards.

    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ellipse area
    Posted in the Geometry Forum
    Replies: 5
    Last Post: August 2nd 2011, 01:36 AM
  2. ellipse area
    Posted in the Geometry Forum
    Replies: 6
    Last Post: November 17th 2010, 06:59 AM
  3. area of ellipse
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 1st 2009, 10:22 PM
  4. Area of an Ellipse
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 1st 2008, 11:36 PM
  5. Area bounded by the ellipse
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 27th 2008, 07:16 AM

Search Tags


/mathhelpforum @mathhelpforum