Fit that Curve, Part 2

Geometry Level 5

Find the largest positive integer \(n\) such that we can fit a conic through any \(n\) points in \(\mathbb{R}^2\).

Clarification: A conic is a curve in \(\mathbb{R}^2\) given by an equation of the form \(c_1+c_2x+c_3y+c_4x^2+c_5xy+c_6y^2\)\(=0\), where at least one of the coefficients \(c_k\) is nonzero.

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