Maximum of three normals pass through point inside parabola proof (1 Viewer)

FootballRobotic

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RTP: From any point located inside the parabola, a maximum of three normals pass through it.
 

braintic

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The equation of the normal is cubic in t. Hence it has up to three real roots (dependent on the value of the point [x,y] you substitute into the normal equation), each root (value of t) corresponding to a point on the parabola.
 

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