Define the Intersection points of polynomials

I am facing the following problem.

Let’s consider 2 points that are not known (x_{0},y_{0}) and (x_{1},y_{1})

I know that from these 2 unknown points (x_{0},y_{0}) and (x_{1},y_{1}) a number of second degree polynomials passes.

f_{i}(x)=a_{i2}x^{2}+a_{i1}x+a_{i0}

For each of these polynomials I know

one point (x_{ki},y_{ki}) of the polynomial and its leading coefficient i.e. a_{i2} which is different for each polynomial.

Is it possible to find the intersection points (i.e. the 2 unknown points) of the aforementioned polynomials?

Re: Define the Intersection points of polynomials

In fact what you want to know is a bit confusing. please elaborate a bit and show the effort you have made so far.

Re: Define the Intersection points of polynomials

Okay, I ll try to elaborate.

I want to define the intersection points of polynomials of degree 2.

In specific I know that a number of polynomials lets say 4 quadratics intersect at 2 points.

The intersection points are not known.

From each of the 4 quadratics I know their leading coefficient and a point. (The known point is different than the intersection point.)

Can I define their intersection points or not?

Re: Define the Intersection points of polynomials