Understanding $a$ and $b$ variables in curve functions

Question

When reading curve formulas I often see letters such as "$a$", "$b$" or "$c$". Im not sure what those mean.

For example the serpentine function:

$y = \frac{abx}{x^2 + a^2}$

What are $a$ and $b$?

Answer 1

Essentially, they represent any numbers. So you could take $a=2$ and $b=5$ and the equation would be $$y=\frac{10x}{x^2+4}\ ,$$ which would be one example of a Serpentine curve. You could get another example by taking $a=4$ and $b=7$, and so on.

Sometimes you will find that there are restrictions on the values of $a$ and $b$. For example, in the article you linked, it specifies that $ab>0$. This is OK in my example because $ab=10$ and $10>0$. But it would not be legitimate to take, for example, $a=3$ and $b=-4$.