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July 8th, 2013, 04:24 PM  #1 
Member Joined: Jun 2013 Posts: 42 Thanks: 0  Find the diff equation of family of circles with center on t
Find the diff equation of family of circles with center on the line y= x and passing through the origin. I'm good in differentiating... but my problem is that if the equation to be differentiated is not given at the start like this worded problem... I know that the eq of circle. is (xh)^2 + (yk)^2 =r^2.... but I don't know how to use the given... line y=x ..... and how to substitute this given line in this equation... can someone give me the proper equation for this problem??.. don't worry I just need the first equation... I will be the one to differentiate . 
July 8th, 2013, 05:40 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find the diff equation of family of circles with center
I would try letting the center of the circle be .

July 9th, 2013, 11:46 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Find the diff equation of family of circles with center
A circle with center at (h, h) (on y= x as MarkFL suggests, would have equation of the form . The distance from (h, h) to (0, 0) is, of course, so : . Multiplying that out, . Then a wonderful thing happens  all those terms cancel! . Now, . Differentiating with respect to x, the constant, h, will disappear. 
July 9th, 2013, 12:52 PM  #4 
Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0  Re: Find the diff equation of family of circles with center @HallsOfIvy : You made a mistake, it should be as above. 

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