text: • Jul 23rd 2011, 07:33 AM
  kakatomy
  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.
  • Jul 23rd 2011, 10:34 AM
  waqarhaider
  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
  • Jul 23rd 2011, 12:46 PM
  Siron
  Where's $\theta$ in the equation? A polar equation looks like: $r=f(\theta)$ but I don't see $\theta$ anywhere.
  • Jul 23rd 2011, 10:45 PM
  kakatomy
  Quote:
  
  Originally Posted by Siron
  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.
  • Jul 23rd 2011, 10:48 PM
  kakatomy
  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.
  • Jul 24th 2011, 10:43 AM
  waqarhaider
  $r=\frac{l}{1-ecos\Theta}$
  is polar equation of conic and represent ellipse if e<1 with foci at
  $\Theta=0$ and $\Theta=\pi$
  • Jul 24th 2011, 11:29 AM
  Siron
explanation: The document contains a math question and a subsequent answer. The question asks to sketch a curve given in polar coordinates and to prove that the curve is an ellipse, identifying its foci. The answer provides a detailed explanation of how to rearrange the given equation and compare it to the standard form of a conic section in polar coordinates to show that it represents an ellipse.
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  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: • Jul 23rd 2011, 07:33 AM
  kakatomy
  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.
  • Jul 23rd 2011, 10:34 AM
  waqarhaider
  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
  • Jul 23rd 2011, 12:46 PM
  Siron
  Where's $\theta$ in the equation? A polar equation looks like: $r=f(\theta)$ but I don't see $\theta$ anywhere.
  • Jul 23rd 2011, 10:45 PM
  kakatomy
  Quote:
  
  Originally Posted by Siron
  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.
  • Jul 23rd 2011, 10:48 PM
  kakatomy
  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.
  • Jul 24th 2011, 10:43 AM
  waqarhaider
  $r=\frac{l}{1-ecos\Theta}$
  is polar equation of conic and represent ellipse if e<1 with foci at
  $\Theta=0$ and $\Theta=\pi$
  • Jul 24th 2011, 11:29 AM
  Siron
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a subsequent answer. The question asks to sketch a curve given in polar coordinates and to prove that the curve is an ellipse, identifying its foci. The answer provides a detailed explanation of how to rearrange the given equation and compare it to the standard form of a conic section in polar coordinates to show that it represents an ellipse.
  
  Label: question-and-answer