What kind of parabola is that?

Geometry Level 5

We all know that a parabola is defined as the set of points equidistant from a point (the focus) and a line (the directrix). But...

The set of points that are equidistant from the line \(y=0\) and the point \((2,3)\) or the point \((2,4)\) can be represented by the equation

\[x^4+ax^3+bx^2+cx+dx^2y+fxy+gy^2+hy+j=0\]

Find \(j\)

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