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/((x3)^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 (xh)^2/a^2+(yk)^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 graphplotting 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  
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 140  Re: How to sketch this function Quote:
 
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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