Ellipse construction from foci and normal line?

rickhg12hs shared this question 4 years ago
Answered

Given the foci of an ellipse and a line that is normal to the ellipse, how can the ellipse be constructed using GeoGebra?

Comments (5)

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Use the optical properties of the ellipse to find the point in which the normal intersects the ellipse.

If n is the normal, F1 and F2 the foci, then the point T on n is such that angle (F1 T n) is congruent to angle (n T F2).

This means that n is the angle bisector of F1 T F2.

When you know T, you also know the (constant) sum of distances that defines the ellipse as locus of points. You can now construct the ellipse using an equation or as a locus of points.

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Yes, you are correct.


But how does one use GeoGebra to select this "T"?

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Brilliant!


I only wish I understood the principles behind this construction.

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@noel : I'm a rebel, never do homework! Bwahaha....

@rick* : I was worried whether in Eng the property I used had the same name as in Italy. Here it is a reference page about what I was talking about.

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Ahhh, beginning to understand. Thanks!

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