Good evening.
There are different parabolic curves which have the same equation for the same value in parameter.
For example. For $n = 2$:
$$299 = 4n^2 + 44n + 195 $$
and,
$$299 = 4n^2 + 56n + 171$$
the line which intersects these parabolic curves at point $(2,299)$ has a equation of $2n+295$.
I can calculate the tangent between these curves by:
$(195 - 171) / (44 - 56) = -2 $; which is the negative value for the $2n+295$, I mean here the tangent is $2$.
My question is the following one: How can I auto-generate different parabolic curves when I have the desired tangent, like the $-2$ above described ?