Consider the problem of fitting a conic through m given points P1(x1, y1), . . . , Pm(xm, ym) in the plane; see Exercises 53 through 62 in Section 1.2. Recall that a conic is a curve in ℝ 2 that can be described by an equation of the form f (x, y) = c1 + c2x + c3 y + c4x2 + c5xy + c6 y2 = 0, where at least one of the coefficients ci is nonzero.
How many conics can you fit through four distinct points P1(x1, y1), . . . , P4(x4, y4)?
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