Question
Thu September 17, 2009 By:

diffrentiation

Expert Reply
Wed September 23, 2009

(x-a)2 + (y-b)2 = c2

Differentiating,

2(x-a) + 2(y-b)dy/dx = 0

Differentiating again,

2 + 2(yd2y/dx2 + (dy/dx)2) = 0

d2y/dx2 = -1/y - (dy/dx)2/y = - (1+(dy/dx)2)/y

Also,
dy/dx = -(x-a)/(y-b)

(dy/dx)2 = (x-a)2/(y-b)2

Using these results,

[1+ (dy/dx)2]/ (d2y/dx2) = [1+ (dy/dx)2]/ (- (1+(dy/dx)2)/y) = - y   

Hence proved.

Regards,

Team,

TopperLearning.

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