Find all functions in 1. quadrant which tangts form triangles

[skrat]

Homework Statement

Find all functions for which any tangent in first quadrant "forms" a triangle with constant surface P. (You can assume that y'<0)

Homework Equations

The Attempt at a Solution

Now, I know I should somehow get to differential equation and then solve it but, I haven't got a clue on how to start?

Tangent is a linear function with $k=\frac{y_2-y_1}{x_2-x_1}$ and also equal to $k=y^{'}(x)$..

That is in fact everything I have so far. I've been staring and this problem for quite a while now. Please help.

 

[haruspex]

Take a point on the curve, y = f(x). Where does the tangent at that point intersect the axes?