1. The problem statement, all variables and given/known data Obtain the differential equation of the family of plane curves described: Circles tangent to the x-axis. 2. Relevant equations [itex](x-h)^2 + (y-k)^2 = r^2[/itex] 3. The attempt at a solution I tried to answer this question using the same way I did on a problem very similar to this (Circles with fixed radius r and tangent to the x-axis), but now I'm getting a different answer. The answer provided by the book for the problem above is [itex][1+(y')^2]^3 = [yy''+1+(y')^2]^2[/itex]. I have no idea how it's done. I want to ask the difference between the ways of how to solve these two problems: (1) circles tangent to the x-axis. (2) circles with fixed radius tangent to the axis. I can solve question (2) because of the hint that [itex]h=r[/itex], but doing the same with question (1) doesn't seem to work and it's making me crazy already. Please give me some clue on how to solve this one. Thanks a bunch!