The length of the subtangent at any point of | vedclass

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(B) Given the curve equation: $x^m y^n = a^{m+n}$.Taking the natural logarithm on both sides: $m \ln x + n \ln y = (m+n) \ln a$.Differentiating with r

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Abscissa

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(B) Given the curve equation: $x^m y^n = a^{m+n}$.Taking the natural logarithm on both sides: $m \ln x + n \ln y = (m+n) \ln a$.Differentiating with respect to $x$: $\frac{m}{x} + \frac{n}{y} \frac{dy}{dx} = 0$.Thus,$\frac{dy}{dx} = -\frac{my}{nx}$.The length of the subtangent is given by the formula: $LST = |\frac{y}{dy/dx}|$.Substituting the derivative: $LST = |\frac{y}{-my/nx}| = |\frac{nx}{m}|$.Since $n$ and $m$ are constants,$LST \propto x$.Here,$x$ represents the abscissa of the point.Therefore,the length of the subtangent is proportional to the abscissa.

The length of the subtangent at any point of the curve $x^m y^n = a^{m+n}$ is proportional to -

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