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Topic: How we get a Ellipse from a Conic, and how we get a Oval from
Cylinder Sections-- knifes that are V and asymmetrical V shaped

Replies: 27   Last Post: Oct 8, 2017 12:41 AM

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 Me Posts: 1,716 Registered: 1/23/16
Re: How we get a Ellipse from a Conic, and how we get a Oval from
Cylinder Sections-- knifes that are V and asymmetrical V shaped

Posted: Oct 5, 2017 5:47 PM

On Thursday, October 5, 2017 at 10:11:12 PM UTC+2, Dan Christensen wrote:

> Archie, for \$52.49, you can save yourself all this embarrassment. Order the
> "Conic Sections Model" made of transparent plastic. See for yourself -- no
> knives or scissors required -- that at an ellipse is indeed a conic section.

Actually, he could save some money by trying to understand a simple proof/demonstration (the core of which is consisting of just 3 lines!):

...

From r(x) = a - ((a-b)/h)x and d(x) = a - ((a+b)/h)x we get that y(x)^2 =
= r(x)^2 - d(x)^2 = ab - ab(2x/h - 1)^2 = ab(1 - 4(x - h/2)^2/h^2. Hence
(1/ab)y(x)^2 + (4/h^2)(x - h/2)^2 = 1, which is the equation of an ellipse.