Find the value of `n in N` such that the curve `(x/a)^n+(y/b)^n=2` touches the straight line `x/a+y/b=2` at the point `(a , b)dot`

Explanation

Now,`(frac{x}{a})^{n}+(frac{y}{b})^{n}=2`

`frac{n}{a}(frac{x}{a})^{n-1}+frac{n}{b}(frac{y}{b})^{n-1} frac{d y}{d x}=0 `

`frac{n}{b}(frac{y}{b})^{n-1} frac{d y}{d x}=frac{-n}{a}(frac{x}{a})^{n-1} `

`frac{d y}{d x}=frac{-n}{a}(frac{x}{a})^{n-1} times frac{b}{n}(frac{b}{y})^{n-1}=frac{-b}{a}(frac{b x}{a y})^{n-1}`

Slope of tangent `=(frac{d y}{d x})_{(a, b)}=frac{-b}{a}(frac{b * a}{a * b})^{n-1}=frac{-b}{a} ldots(2)`

The equation of tangent is


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