If the subnormal at any point on the curve y^ | vedclass

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Question

(B) Given the equation of the curve is $y^n = ax$. Differentiating both sides with respect to $x$,we get: $n y^{n-1} \frac{dy}{dx} = a$ $\frac{dy}{dx}

Vedclass · Accepted Answer

$2$

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(B) Given the equation of the curve is $y^n = ax$. Differentiating both sides with respect to $x$,we get: $n y^{n-1} \frac{dy}{dx} = a$ $\frac{dy}{dx} = \frac{a}{n} y^{1-n}$ The length of the subnormal is defined as $|y \frac{dy}{dx}|$. Substituting the value of $\frac{dy}{dx}$: $	ext{Length of subnormal} = |y \cdot \frac{a}{n} y^{1-n}| = |\frac{a}{n} y^{2-n}|$. For the subnormal to be constant,it must be independent of the variable $y$. This occurs when the exponent of $y$ is $0$,i.e.,$2 - n = 0$. Therefore,$n = 2$. Hence,the correct option is $B$.

If the subnormal at any point on the curve $y^n = ax$ is constant,then the value of $n$ is:

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