The equation of the family of curves for which length of the sub normal at any point $(\mathrm{x}, \mathrm{y})$ is always a constant $(\mathrm{k})$ is

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Aicharya · Accepted Answer

Length of subnormal is $(\mathrm{y}, \mathrm{m})=\mathrm{k}$ $\begin{aligned} & \mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}= \pm \mathrm{k} \ & \mathrm{ydy}= \pm \mathrm{kdx} \ & \frac{\mathrm{y}^2}{2}= \pm \mathrm{kx} \ & \mathrm{y}^2= \pm 2 \mathrm{kx}+\mathrm{A} \ & \mathrm{y}^2-\mathrm{A}= \pm 2 \mathrm{kx}\end{aligned}$

The equation of the family of curves for which length of the sub normal at any point $(\mathrm{x},…

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