Can you Find the Focal points of an Ellipse?

Using the Xara ellipse too, create a Red ellipse of width (major axis) 400px and height (minor axis) 200px.

Attachment 122804

The Challenge is to find the focal points F1 & F2 without any calculation.

Your "proof" will be any triangle with a base of F1F2 (346.4px) and apex on the rim of the ellipse will have a Perimeter of 746.4px.

P(F1AF2) = P(F1BF2) = P(F1CF2).

Knowing the length between the focal points and with a rope or twine the length of the perimeter and tied into a single loop, it would be possible to inscribe the ellipse to be the basis of an elliptical pond or garden feature.

The path from one focus to the rim to the other focus is always goings to be 400px.
This is the reason whispering galleries work; any sound made at either focus is concentrated at the other one.

Acorn

This time I try to attach a video with my solution...

Marco.

Quote:

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Originally Posted by Marco D

This time I try to attach a video with my solution...
Marco.

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Nice to watch Marco.

You are solving these faster than I can make them!

My solution uses the ellipse, a circle and a line.

1. Create a Green circle, a Blue Line and a Red ellipse, all 400px wide; the Red ellipse can be a clone of the Green circle, halving its Height.
2. Place the circle and ellipse bases together; the circle's centre is now on the ellipse edge. the length of a radius to either of the points where the line cuts the circle are, necessarily, 200px. The chord, the line in the green, is what we want.
3. Select the line and circle and Intersect.
4. Switch to the Shape tool after selecting the chord (this is a shape and not a line); it has zero Line size.
5. Click on the chord to add a Node.
6. Drag the Node to any point of the Red ellipse.

Attachment 122809

Instead of a line, I halved a cloned ellipse to the same effect. I found the line solution clearer.

Acorn

Quote:

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Originally Posted by Acorn

Nice to watch Marco.

You are solving these faster than I can make them!

My solution uses the ellipse, a circle and a line.

1. Create a Green circle, a Blue Line and a Red ellipse, all 400px wide; the Red ellipse can be a clone of the Green circle, halving its Height.
2. Place the circle and ellipse bases together; the circle's centre is now on the ellipse edge. the length of a radius to either of the points where the line cuts the circle are, necessarily, 200px. The chord, the line in the green, is what we want.
3. Select the line and circle and Intersect.
4. Switch to the Shape tool after selecting the chord (this is a shape and not a line); it has zero Line size.
5. Click on the chord to add a Node.
6. Drag the Node to any point of the Red ellipse.

Attachment 122809

Instead of a line, I halved a cloned ellipse to the same effect. I found the line solution clearer.

Acorn

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You solution is indeed clearer. I hadn't tought interecting a line with a shape (the circle in this case), good to know!
Next time I'll try to wait a bit longer before posting my solutions ;)

Marco.

https://vimeo.com/303752260

Quote:

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Originally Posted by gwpriester

https://vimeo.com/303752260

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Thank you Gary. clearly Maxim has been following my Threads here.

It is amazing what can be done with the Xara Desktop applications.

Acorn