Parabola

[jim k]

I am using a CAD system to create a parabola for a solar reflector. My first attempt was to create a cone and take a cut of it with a plane parallel to the axis of the cone. I attempted to test the result by creating lines parallel to the center line of the parabola simulating the rays of the sun. I did this by creating a line tangent to the parabola at the intersection point of each of the rays with the parabola. I then measured the angle of incidence from the ray line to the tangent line and duplicated that angle as I created a reflect line with the same angle through the same point. the resulting reflect lines do not meet at a common point, not even close.
I then created a parabola using the equation for a parabola and tested it the same way. All of reflect lines intersected the same point perfectly.
My question is, why did the CAD generated parabola from a conic section not result in a common focal point?

[Guest]

http://img.tfd.com/ggse/75/gsed_0001_0013_0_img3110.png
A parabola is formed by taking the cross-section of a cone where the plane is parallel to the cone's "slanted edge" see picture (b) in the link above. If you take the plane parallel to the axis you get a hyperbola see picture (c).

Hope this helps,

R. Baber.

[jim k]

Thanks that makes sense.

[Guest]

Hey
If a is the semi-major axis and b is the semi-minor axis, then c is the focal radius, where d1 + d2 = 2a, and c2=a2-b2