Prove that `(x/a)^n+(y/b)^n=2` touches the straight line `x/a+y/b=2` for all ` in N` , at the point `(a ,\ b)` .

Explanation

`n(x/a)^(n-1)*1/a+n(y/b)^(n-1)*1/b*dy/dx=0`

`dy/dx=(-n(x/a)^(n-1)*(1/a))/(n(y/b)^(n-1)*(1/b)`

`=(-b(x/a)^(n-1))/(a(y/b)^(n-1))`

`-b/a((x/a)^(n-1)/(y/b)^(n-1))=-b/a`

`y-b=-b/a(x-a)`

`y/b-1=-x/a+1`

`x/a+y/b=2`.