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find the differential equation of all circles which pass through the origin and whose center lies on xaxis

1 Answer

All circles passing through origin and having centre on $X-axis$ say at $(a,0)$ will have $ radius= a$
$\therefore $ General equation of such circles is
This equation has only one arbitrary constant.$a$.
$\therefore$ This equation can be differentiated only once to remove the arbitrary constant $a$
Differentiating (i) on both the sides we get
Substituting the values of $(x-a) \:\:and\:\: a$ in (i) we get
is the differential equation of the given circles.
answered Dec 13, 2013 by rvidyagovindarajan_1