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![[Post New]](/templates/default/images/icon_minipost_new.gif) 25 Mar 2007 01:25:42 IST
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The diff. Eqn of the family of circles having the centres on the Y-axis:-
(a) xd2y/dx2-(dy/dx)3-dy/dx=0
(b) xd2y/dx2+(dy/dx)3+dy/dx=0
(c) d2y/dx2-(dy/dx)3-xdy/dx=0
(d) d2y/dx2+(dy/dx)3+xdy/dx=0
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25 Mar 2007 06:15:59 IST
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A is the answer
let center be (0,a)
eq of circle x2+(y-a)2=r2
differentiating
2x+2(y-a)dy/dx=0
or dy/dx= -x/(y-a) -------------1
again differtiating this
2+2(dy/dx)2+2(y-a)d2y/dx2=0
multiplying x/(y-a) in this eq
we get
x/(y-a) +x/(y-a)(dy/dx)2+xd2y/dx2=0
replace x/(y-a) by -dy/dx as by eq 1
we get xd2y/dx2-(dy/dx)3-dy/dx=0
as answer
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