Sunday, 18 August 2013

Find the differential equation for a family of curves

Find the differential equation for a family of curves

The problem is stated as follows:
Find the ordinary differential equation for the family of circumferences
with radius equal to $1$ and whose center is in the circumference
$$x^2+y^2=25$$
Any ideas? I got so far as to determine that $h^2+k^2 = 25$ so that the
circumference's equation is defined as $(x-h)^2+(y-\sqrt{25-h^2})^2=1$
form there I'm not sure what I should do.
Thanks in advance.

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