Trace a path into a curve

holyfssssd shared this question 4 months ago
Needs Answer

I have the following setup:https://www.geogebra.org/cl...

As you move point G from D to C, point H will move along a path tracing a certain kind of curve.

Is there a way to convert this path into a proper curve parameter?

Comments (8)

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it is a part of cardioid

/rEpEjYhefxkAAAAASUVORK5CYII=

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Thank you, what kind of equation did you use?

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Ah, I think I figured it out, it's Locus(H,G) right?

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Ok, the locus method works well in this case, but it becomes too laggy when there's a high quantity of them. Is there a way to use the cardioid equation? I tried to look up the equation, but I can't figure out how to fit the curve into my setup. Can anyone help me with this?

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What's the equation?

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The equation seems to be:

(x^2+y^2-2ax)^2=4a^2.(x^2+y^2)
Here's a few examples I found:

https://www.geogebra.org/classic/B4esju2T

https://www.geogebra.org/classic/qmcpqmud

But there's also this one which uses

Curve(cos(s) (1-cos(s)),sin(s) (1-cos(s)),s,0,t)
https://www.geogebra.org/classic/dTw7UQEj

This site also lists other equations:

http://xahlee.info/SpecialP...

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This looks fine, try that inside Sequence()

Curve(cos(s) (1-cos(s)),sin(s) (1-cos(s)),s,0,t)

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How do I make the curve automatically match loc1 here? (even if you move point F):

https://www.geogebra.org/cl...

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