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Math Help - a question about ellipse

  1. #1
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    a question about ellipse

    Sketch the curve given in polar coordinates by the equation:

    r= (2a) / (3+2cos x)

    Prove that this curve is an ellipse and identify its foci.

    *From a Further pure maths book.

    Thanks brothers.
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  2. #2
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    Re: a question about ellipse

    your equation can be arranged as

    r = (2a/3) / [1 + (2/3)cos x] now comparing with polar equation of conic r = l / ( 1 + ecos x)

    we get eccentricity e = 2/3 < 1 so represent ellipse with foci at pole and ( 2a,pi ) where l = 2a/3 is semi latusrectum
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: a question about ellipse

    Where's \theta in the equation? A polar equation looks like: r=f(\theta) but I don't see \theta anywhere.
    Last edited by Siron; July 23rd 2011 at 02:24 PM.
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    Re: a question about ellipse

    Quote Originally Posted by Siron View Post
    Where's \theta in the equation? A polar equation looks like: r=f(\theta) but I don't see \theta anywhere.

    sorry i dun know how to type the theta out but the x is the theta.
    thanks brother.

    btw hows the sketching of the curve?
    i dun even know wt it is.
    thanks bro.
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  5. #5
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    Re: a question about ellipse

    r = l / ( 1 + ecos x)
    the ' l ' means?

    i am not good at maths. not reli understand the idea, thanks brother helping me to further explain. thanks.
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  6. #6
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    Re: a question about ellipse

    r=\frac{l}{1-ecos\Theta}
    is polar equation of conic and represent ellipse if e<1 with foci at
    \Theta=0 and \Theta=\pi
    Last edited by waqarhaider; July 25th 2011 at 04:03 AM. Reason: latex not used properly
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: a question about ellipse

    If you want to work with latex you have to use [ tex ] ... [/ tex], not [ Tex] ... [/ Tex ]
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