The length of the subnormal to any point of a | vedclass

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(D) The length of the subnormal at any point $(x, y)$ on a curve is given by the formula $L = |y \frac{dy}{dx}|$. Given that the length of the subnorm

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$e = 1$

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(D) The length of the subnormal at any point $(x, y)$ on a curve is given by the formula $L = |y \frac{dy}{dx}|$. Given that the length of the subnormal is constant,let $L = k$,where $k$ is a constant. Thus,$|y \frac{dy}{dx}| = k$. Assuming $y > 0$,we have $y \frac{dy}{dx} = k$. Integrating both sides with respect to $x$: $\int y \, dy = \int k \, dx$. This gives $\frac{y^2}{2} = kx + C$. For simplicity,let $C = 0$,so $y^2 = 2kx$. This is the equation of a parabola. The eccentricity of a parabola is $e = 1$.

The length of the subnormal to any point of a curve is constant. Then,the eccentricity of the curve is . . . . . .

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