1that's wat i did.. the book's given a diff solution...
Show that the curve (x/a)2n + (y/b)2n=2 touches the straight line x/a+y/b=2 at (a,b) no matter what the value of n be.
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3 Answers
62I dont know the problem with this problem :P
you have to show that dy/dx at a,b is equal to -b/a
\\(x/a)^{2n}+(y/b)^{2n}=2 \\1/a\times2n(x/a)^{2n-1}+1/b\times2n(y/b)^{2n-1}dy/dx=0 \\1/a\times2n(a/a)^{2n-1}+1/b\times2n(b/b)^{2n-1}dy/dx=0 \text{(Substituting x=a, y=b)} \\1/a+1/bdy/dx=0 \text{(Substituting x=a, y=b)}
Hence proved :)
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