I have been thinking about the following problem. I have a curve in 2D space (x,y), described by the following equation: where a,b,c,d are known. It is obvious that it is a 1D curve embedded in a 2D space. So I would think there could be such a description of the curve, where only single parameter is present.
It is obvious that you can plug x and then solve a quadratic equation for y, but that is not what I'm looking for. The solution I expect is in the form
which can be used in the case of circle equation with sine and cosine of angle.
My goal is to plot the curve in python, so I would like to start at some point of the curve and trace along it. Could you point me to a solution or some materials which are dedicated for such problems?