1. The problem statement, all variables and given/known data Find the implicit equation of the curve that goes through the point (3, 1) and whose tangent and normal lines always form with the x axis a triangle whose area is equal to the slope of the tangent line. Assume y` > 0 and y > 0. 2. Relevant equations Hint: ∫( √(a^2 - u^2) / u du = √(a^2-u^2) - a*ln | [a+√(a^2-u^2)] / u | + C (sorry, I don't know how to use the math writer yet) 3. The attempt at a solution This is a question from an introductory differential equations class. I have absolutely no idea how to do this! I haven't really gotten anywhere yet. This is what I've done: let f(x) denote the curve we're looking for. Then the tangent line will have equation: y_t = df/dx * x + C Normal line will have equation y_n = -1/(df/dx) * x + k Together they will form a triangle with area = df/dx, at any point on f(x). I wanted to find an expression for area in terms of df/dx, simplify it, and solve the resulting differential equation, but I can't figure out a DE for the area! I'm getting very frustrated, as we've never been shown a question like this in lecture, and I can't find any examples in my textbook. Help would be very much appreciated!