In the figure below, a curve passes through $(3,1)$. The length of the normal $P C$ through any point to the $x$-axis is equal to twice the ordinate of that point, for $y0$. The equation for the distance PC for any curve is given by $P C=y \sqrt{1+\left(y^{\prime}\right)^{2}}$. Find the equation of this curve.

Question

In the figure below, a curve passes through $(3,1)$. The length of the normal $P C$ through any point to the $x$-axis is equal to twice the ordinate of that point, for $y>0$. The equation for the distance PC for any curve is given by $P C=y \sqrt{1+\left(y^{\prime}\right)^{2}}$. Find the equation of this curve.

Quizplus · Accepted Answer

The Answer of In the figure below, a curve passes through $(3,1)$. The length of the normal $P C$ through any point to the $x$-axis is equal to twice the ordinate of that point, for $y>0$. The equation for the distance PC for any curve is given by $P C=y \sqrt{1+\left(y^{\prime}\right)^{2}}$. Find the equation of this curve.

In the Figure Below, a Curve Passes Through (3,1)(3,1)(3,1) the Length of the Normal

In the Figure Below, a Curve Passes Through $(3,1)$ the Length of the Normal