# Calculust-1

Calculus Level 5

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, $$e=2.718\ldots$$.
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