Prove that curve(x/a)n+(y/b)n=2 touches the straight line x/a+y/b=2 at (a,b) for all values of n belongs to N at the point (a,b)..

Equation of the given curve is

Differentiating both sides w.r.t x, we get

Equation of tangent at (a, b) is

Thus, the given curve touches the line at (a, b) ∀  n N

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