When I was young I used to draw a sequence of straight lines on graph paper which made a curve after I finished. On a coordinate plane, the lines would be equivalent to starting at $y=9$ on the $y$ axis and ending at $x=1$ on the $x$ axis. With each line, I would decrease the $y$ by one unit and increase the $x$ by one unit.
Here is a desmos graph that illustrates. https://www.desmos.com/calculator/u4ea8swmfg
Here is a similar example where the angle between the lines is 60 degrees. https://drive.google.com/open?id=0B5QHq_oPha0ybGdrbFNhUHRPOGc
I think each line is basically a tangent line along the curve produced by taking a first derivative.
Are these types of curves parabolas or possibly hyperbolae? And how could I find the equation of such a curve?