Let S be the set of all the natural numbers, for which the line (x/a)+(y/b)=2 is a tangent to the curve (( x / a )) n +(( y / b )) n =2 at the point (a, b), a b ≠ 0. Then:

Question

Let S be the set of all the natural numbers, for which the line (x/a)+(y/b)=2 is a tangent to the curve (( x / a )) n +(( y / b )) n =2 at the point (a, b), a b ≠ 0. Then: (A) S=φ (B) n ( S )=1 (C) S = 2 k: k ∈ N  (D) S = N

Tardigrade Admin · Accepted Answer

(( x / a )) n +(( y / b )) n =2 Slope of tangent at (a, b) n ⋅((x/a))n-1 ⋅ (1/a)+n((x/b))n-1 ⋅ (1/b) (d y/d x)=0 .( dy / dx )|(a, b)=-( b / a ) ∴ Equation of tangent y-b=-(b/a)(x-a) ( x / a )+( y / b )=2 ∀ n ∈ N

Q. Let $S$ be the set of all the natural numbers, for which the line $\frac{x}{a} + \frac{y}{b} = 2$ is a tangent to the curve $(\frac{x}{a})^{n} + (\frac{y}{b})^{n} = 2$ at the point $(a, b), ab \neq = 0$ . Then:

$S = ϕ$

$n (S) = 1$

$S = {2 k : k \in N}$

$S = N$

Q. Let S be the set of all the natural numbers, for which the line ax​+by​=2 is a tangent to the curve (ax​)n+(by​)n=2 at the point (a,b),ab=0. Then:

S=ϕ

n(S)=1

S={2k:k∈N}

S=N

(ax​)n+(by​)n=2 Slope of tangent at (a,b) n⋅(ax​)n−1⋅a1​+n(bx​)n−1⋅b1​dxdy​=0 dxdy​∣∣​(a,b)​=−ab​ ∴ Equation of tangent y−b=−ab​(x−a) ax​+by​=2∀n∈N

Q. Let $S$ be the set of all the natural numbers, for which the line $\frac{x}{a} + \frac{y}{b} = 2$ is a tangent to the curve $(\frac{x}{a})^{n} + (\frac{y}{b})^{n} = 2$ at the point $(a, b), ab \neq = 0$ . Then:

$S = ϕ$

$n (S) = 1$

$S = {2 k : k \in N}$

$S = N$