Fit that curve!

Geometry Level 4

True or false:

\(\quad\) We can fit a cubic through any nine points in \(\mathbb{R}^2\).

Clarification: A cubic is a curve in \(\mathbb{R}^2\) given by an equation of the form \(c_1+c_2x+c_3y+c_4x^2+c_5xy+c_6y^2+c_7x^3\)\(+c_8x^2y\)\(+c_9xy^2+c_{10}y^3\)\(=0\), where at least one of the coefficients \(c_k\) is nonzero.

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