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`

Options

A. 2
B. 3
C. 4
D. any real number

Answer

D

Explanation

Given `(x/a)^(n)+(y/b)^(a)=2`
`:.1/(a^(n))nx^(n-1)+1/(b^(n))ny^(n-1)y'=0`
`implies y'=(-b^(n))/(a^(n)). (x^(n-1))/(y^(n-1))`
At `(a,b),y'=(-b^(n))/(a^(n)). (a^(n-1))/(b^(n-1))=(-b)/a`
Hence it is independent of `n`.