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April 5th, 2010, 05:47 AM   #1
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How to sketch this function

Hi,

I'm not very sure of where this belongs but here it goes:
How do I sketch this family of functions?

(-1/((x+3)^2+y^2)^.5)-(1/((x-3)^2+y^2)^.5)= Constant
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April 6th, 2010, 08:05 AM   #2
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How would you usually plot families of ellipses?
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April 6th, 2010, 11:15 AM   #3
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Re: How to sketch this function

I would put them in the form (x-h)^2/a^2+(y-k)^2/b^2=1 and plot. I would put (h,k) in the center and then draw the major and minor axis.
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April 7th, 2010, 07:19 AM   #4
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Have you tried to manipulate the equation you were given into a simpler form?
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April 8th, 2010, 04:14 AM   #5
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Re: How to sketch this function

Yes but the simpler form continues to be too hard to be sketched
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April 8th, 2010, 04:37 AM   #6
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It may take a little ingenuity to get a sufficiently simple form. I made an attempt and failed, but could easily have missed something. Using graph-plotting software, I can't distinguish by eye the ellipses generated from ones generated directly from the usual equation for an ellipse.
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April 8th, 2010, 08:18 AM   #7
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Re: How to sketch this function

Quote:
Originally Posted by kolg
Hi,

I'm not very sure of where this belongs but here it goes:
How do I sketch this family of functions?

(-1/((x+3)^2+y^2)^.5)-(1/((x-3)^2+y^2)^.5)= Constant
I don't think these are ellipses. When I graphed these for various values of the constant I got curves which look like Cassinian Ovals. Perhaps a switch to polar coordinates might be helpful.
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April 10th, 2010, 08:21 AM   #8
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The ovals are not quite ellipses, and they are very similar to Cassinian ovals.
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