I have two algebraic curves as the following
\begin{equation}
2x^2+4x-3-y=0\quad(1)
\end{equation}
x^2+y^2-a=0\quad\qquad(2)
Equation (2) is parameterized in terms of a. I am interested to obtain the number of intersections between curves (1) and (2) as the parameter a changes.
I thought of formulating the problem as follows:
If a has an initial interval of
a=interval(-10,10);
Then what are the intervals where curves 1 and 2 have exactly four intersections? I have reviewed IntervalArithmatic and IntervalConstraintProgramming packages and not sure if I can find a solution to this. I would be deeply greatful to any pointers.
Thanks in advance!