This applet uses some nice features of Geogebra 4 (including multivariable functions) to create an interactive worksheet that can be used to investigate how many normals to [math] go through a specified point.
The general question involves generating and solving a cubic, but with care students can investigate sub-problems that only involve solving quadratics. As an investigation it is suitable for an advanced A-level class.
Normals to a Quadratic through a Given Point
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Comments (2)
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Very interesting. I have been trying to trace the normals to an ellypse from an external point. I found an old method by Apolonio, using an equilateral hyperbola (search in GG tube my upload APOLONIO'S NORMAL TO AN ELLIPSE). But Apolonio's method doesn't work for all positions of the point. I'd thank any idea about a general method. Thanks.
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The exact title of my upload is "NORMAL TO AN ELLIPSE BY APOLONIO OF PERGE"