The sub-tangent at any point of the curve x-m-y-n- a-m-1-varies as-Abscissa-2-Abscissa-3-Abscissa-Ordinate-

The correct option is C Abscissa We have, x^m y^n = a^m+1 ⇒ m log x + n log y = (m + 1)log a ∴m/x + n/ydy/dx = 0 ⇒dx/dy = nx/my ∴ Sub tangent = = | y dx/dy ...

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Byju's Answer

Standard XII

Mathematics

Subtangent

The sub-tange...

Question

The sub-tangent at any point of the curve $x^{m} y^{n} = a^{m + 1}$ varies as

$(A b s c i s s a)^{2}$

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$(A b s c i s s a)^{3}$

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Abscissa

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Ordinate

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Solution

The correct option is C
Abscissa

We have, $x^{m} y^{n} = a^{m + 1} \Rightarrow m l o g x + n l o g y = (m + 1) l o g a ∴ \frac{m}{x} + \frac{n}{y} \frac{d y}{d x} = 0 \Rightarrow \frac{d x}{d y} = \frac{n x}{m y} ∴ S u b - t a n g e n t == ∣ ∣ y \frac{d x}{d y} ∣ ∣ = \frac{n x}{m} a x .$
Hence (c) is the correct answer.

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The sub-tangent at any point of the curve xm yn=am+1 varies as

The correct option is C Abscissa We have, xm yn=am+1⇒m log x+n log y=(m+1)log a∴mx+nydydx=0⇒dxdy=nxmy∴Sub−tangent==∣∣ydxdy∣∣=nxm ax. Hence (c) is the correct answer.

The sub-tangent at any point of the curve $x^{m} y^{n} = a^{m + 1}$ varies as