6.12 ** Show that the path y = y(x) for which the integral function. | x/1- y2 dx is stationary is a sinh

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You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. 8. Your design team has coded this in-game world to exist on the circle x² + y? < 900 Page 3 on the xy-plane. At any point (x, y) in this world you've also associated a danger function d(x, y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x, y) correspond to safe points. If d(x, y) = e¬a²y, find the safest point(s) and most dangerous point(s) in-game.

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