The length of sub-tangent to the curve yn=an−1⋅x at (x,y) on it is

yn=an−1x1, dydx=m=ynx⇒m=|ym⇒L.S.T=|nx||

The length of sub-tangent to the curve yn=an−1⋅x at (x,y) on it is

yn=an−1x1, dydx=m=ynx⇒m=|ym⇒L.S.T=|nx||

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The length of sub-tangent to the curve $y^{n} = a^{n - 1} \cdot x at (x, y)$ on it is

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$| \frac{n}{x} |$

$| n x |$

$n^{2} | x |$

$\frac{n^{2}}{| x |}$

answer is B.

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Detailed Solution

$y^{n} = a^{n - 1} x^{1}$ ,

$\frac{d y}{d x} = m = \frac{y}{n x} \Rightarrow m = | \frac{y}{m} \Rightarrow L . S . T = | n x | |$

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The length of sub-tangent to the curve yn=an−1⋅x at (x,y) on it is

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The length of sub-tangent to the curve $y^{n} = a^{n - 1} \cdot x at (x, y)$ on it is