constant tangent curve elements

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I have to write a paper with a title Curves with a constant tangent elements, but I have no idea what those curves are. I have been searching in the literature we've been given, but the truth is I really have no idea what to look for. Please help? The paper is part of differential equations class, if that is of any help. I have to find 4 different examples and solve them.

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Hint

I suggest you have a look at http://hom.wikidot.com/the-tractrix. You will see that these curves obey a quite simple differential equation $$\frac{dy}{dx}=-\frac{y}{\sqrt{a^2-y^2}}$$ which is separable. Using parametrization leads to quite simple equations.