John D. Cook • 4/14/2026

Finding a parabola through two points with given slopes

This article explains how to find the parameters of a parabola that passes through two specified points with given slopes at those points. It begins by discussing the general conic section equation and the parabola condition (b² = 4ac), then shows that the problem has a unique solution. A Python function is provided that computes the six coefficients (a, b, c, d, e, f) of the parabola. The solution is derived from algebraic manipulation and is useful for geometric modeling or interpolation tasks.

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#Python #computational geometry #Geometry