Determinants and Conic Section Curves

Determinants and Conic Section Curves

Background.  

    Five points in the plane uniquely determine an equation for a conic section. The implicit formula for a conic section is often mentioned in textbooks, and the special cases for an ellipse, hyperbola, parabola, circle are obtained by either setting some coefficients equal to zero or making them the same value.

Implicit Equation for a Line.  

    The equation    of the line through the two points    can be computed with the determinant