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**.

**
**