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.