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 April 5th, 2010, 05:47 AM #1 Newbie   Joined: Dec 2009 Posts: 8 Thanks: 0 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
 April 6th, 2010, 08:05 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,627 Thanks: 2077 How would you usually plot families of ellipses?
 April 6th, 2010, 11:15 AM #3 Newbie   Joined: Dec 2009 Posts: 8 Thanks: 0 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.
 April 7th, 2010, 07:19 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,627 Thanks: 2077 Have you tried to manipulate the equation you were given into a simpler form?
 April 8th, 2010, 04:14 AM #5 Newbie   Joined: Dec 2009 Posts: 8 Thanks: 0 Re: How to sketch this function Yes but the simpler form continues to be too hard to be sketched
 April 8th, 2010, 04:37 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,627 Thanks: 2077 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.
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.

 April 10th, 2010, 08:21 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,627 Thanks: 2077 The ovals are not quite ellipses, and they are very similar to Cassinian ovals.

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