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how to join 2 tangents perpendicular to each other
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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
 GeoGebra
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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
Many thanks mate,
i hope ill be able to follow what you did.
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.
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
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.
Perfect! Thanks very much John...your explanation and stating which commands you used helped enormously.
Thanks again
Neil
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