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if x=a sin t – b cos t, y=a cos t+ b sin t , prove that d2y/dx2= -(x^2+y^2/y^3)

if x=a sin t – b cos t, y=a cos t+ b sin t , prove that d2y/dx2= -(x^2+y^2/y^3)

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
x=asint-bcost
y=acost+bsint
squaring and then adding both eqs., we get
x2+y2=a2+b2
Now diff. w. r. to x
2x+2y.dy/dx=0
dy/dx=-x/y
diff .w.r.to x again
d2y/dx2= -{(y.1-x.dy/dx)/y2}
= -{(y+x2/y)/y2}=-(x2+y2)/y3
Thanks & Regards
Rinkoo Gupta
askIITians Faculty

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