CBSE Class 12-science Answered
diffrentiation
Asked by | 17 Sep, 2009, 12:34: PM
Expert Answer
(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.
Answered by | 23 Sep, 2009, 11:40: PM
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