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Maths NCERT Exemplar Solutions Class 12th Chapter Six Straight Lines Ncert Solutions Maths class 11th Maths Class 11th

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 Then

Option 1 -

$S = ϕ$

Option 2 -

n(S) = 1

Option 3 -

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

Option 4 -

S=N

4 Views | Posted 2 months ago

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1 Answer

Answered by

Payal Gupta | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

${(\frac{x}{a})}^{n} + {(\frac{y}{b})}^{n} = 2$

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

$\Rightarrow \frac{d y}{d x} = - \frac{b}{a} {(\frac{b x}{a y})}^{n - 1}$

$\frac{d y}{d x_{(a, b)}} = - \frac{b}{a}$

So line always touches the given curve.

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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 Then

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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), ab Then

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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 Then