Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Are the given below families of curves orthogonal trajectories of each other? (In other words, is every curve in one family orthogonal to every curve in the other family?)
Then the problem goes on to give me five geometric graphs, one of which is presumably the graph of the equations shown above. Other than the fact that we are studying implicit differentiation, which I have attempted with the hope that I would see a negative reciprocal relationship between these two equations, I have no idea how to do this. I did not find a negative reciprocal relationship, so my instinct that these are not orthogonal, but I don't trust my calculations.
Can anybody help?