# Differential equation: elimination of arbitrary constants

Eliminate the arbitrary constants and find the differential equation of the family of circles of fixed radius r with centers on the x-axis

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what have you tried? –  Vijay Raghavan Aug 16 '13 at 14:55
@marlyn: Is that how the question is written and that is all of it? –  Amzoti Aug 16 '13 at 15:07
If you want people to put some effort into answering your question, you should put some effort into asking it. –  Rhys Aug 16 '13 at 15:14
The family of circles having center on $X$ axis is $(x-a)^2+y^2=r^2\cdots(1)$, where $a\in \mathbb{R}$
differentiating with $x$, we get $2(x-a)+2yy'=0\cdots(2)$ eliminating $a$ from (1) and (2), we get $y^2y'^2+y^2=r^2$