how to join 2 tangents perpendicular to each other

neileyre shared this question 5 years ago
Answered

Hi,

My brother recently told me about Geogebra and now im trying to learn how to use it.

I want to plot the locus of the intersection of 2 tangents to an ellipse, the tangents being perpendicular to each other.

The outcome will be a circle.

But I am having difficulty getting the 2 tangent to stick together at 90 degrees, when I move the tangent point around.

If i construct a perp. to one tangent , the line stays through that point and doesnt stay a tangent.

if i construct another tangent , I cant make it stick to the other at 90.


Can anyone help please.

Neil

Comments (6)

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Have a look at the attached worksheet.


Drag point K (on the ellipse) around. The locus of point B describes the circle you're looking for.


John.


Note: because of symmetry, there are an additional 2 tangents (4 with the perpendiculars) than those shown but, I hid those to make things cleaner.

https://ggbm.at/2498791

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Many thanks mate,

i hope ill be able to follow what you did.

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the key to the whole thing is using the command


Tangent[ <Line>, <Conic> ]

Creates (all) tangents to the conic section that are parallel to the given line.


After creating the first two tangents that are parallel to each other (on points N and L), I create line f which is perpendicular to the tangent i then using the command Tangent[f, c] you get the tangents that are parallel to the perpendicular to tangent i.


After that just define point B as the intersection of the tangents perpendicular to each other and voila!


Lines a and b provide the "starting" points to define points for the initial tangents.


You can see and, play all the steps one by one using the construction protocol. Go to View->Construction Protocol. To play the construction steps one by one, select Options->Advanced, on that dialog select the second icon "Preferences - Graphics" and make sure that all the boxes under "Navigation Bar for Construction Steps" are checked. With that, you can see how the example was built step by step.


John.

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hello

why i can not animate K ?


what you did?


i have created several points on several paths in your file and i can not animate anything


saludos

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That's because I have "Use Path and Region Parameters" in the "Preferences - Advanced" set to "off". Set it to "on" and animation will work.


Saludos!


John.

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Perfect! Thanks very much John...your explanation and stating which commands you used helped enormously.

Thanks again


Neil

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