Q. 84.8( 4 Votes )

Form the differential equation corresponding to (x – a)2 + (y – b)2 = r2 by eliminating a and b.

Answer :

(x – a)2 + (y – b)2 = r2 …… (i)

On differentiating with respect to x, we get,




Again, differentiating with respect to x we get,




Put the value of (y – b) obtained in (ii) we get,





Put the value of (x – a) and (y – b) in (i) we get,



Put we get,



(y’3 + y’)2 + (y’2 + 1)2 = r2y’’2


So, the required differential equation is (y’3 + y’)2 + (y’2 + 1)2 = r2y’’2.


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