Calculust-1

A curve passes through $(1,0)$ such that the ratio of the square of the intercept cut by any tangent off the $y$ -axis to the subnormal is equal to the ratio of the product of the co-ordinates of the point of tangency to the product of square of the slope of the tangent and the sub-tangent at the same point.If the equation of the curve is $y=f(x)$ then $y=(e/b)$ at $x=e$ . Then $b$ equals?

Details and Assumptions :

• There are two such possible curves of the form $x=e^{\pm F(x,y)}$ where $F(x,y)$ is a function involving $x$ and $y$ . Use $+F(x, y)$ .
• $e$ is the mathematical constant, $e=2.718\ldots$ .