Equilaterals on a Parabola

★ 7/10Parametrization conic sections analytic geometry Casework

Problem

An equilateral triangle $ABC$ has vertices $A, B$ on the parabola $y^2 = 4x$ and third vertex $C(4, 0)$ . How many such equilateral triangles are there?

Answer

Solution

Difficulty	7/10
Topics	Parametrization, conic sections, analytic geometry, Casework

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