Question about ellipse and chord

[zyxwv99]

I drew an oval using the ellipse tool of a vector-based drawing program. It's 23.5 mm wide and 21.5 mm high. There is a chord 15 mm long perpendicular to the minor axis. So the question is, how do I calculate the distance from the chord to the end of the ellipse (i.e., the end of the major axis).

(By the way, I've been wracking by brains trying to figure out an oval that's just a stretch-out circle could be a conic section. The best I can figure is a cone with an extremely small angle, cut diagonally many miles from the apex.)

http://lightcolorvision.wordpress.com/
(There a diagram near the top of this blog, entitled "Need help on this problem.")

 

[Mark44]

I drew an oval using the ellipse tool of a vector-based drawing program. It's 23.5 mm wide and 21.5 mm high. There is a chord 15 mm long perpendicular to the minor axis.

In the drawing at the blog entry, the chord is actually perpendicular to the major axis.

So the question is, how do I calculate the distance from the chord to the end of the ellipse (i.e., the end of the major axis).

What I would do is figure out the equation of the ellipse, and then determine the coordinates on the ellipse of the endpoints of the chord, given that the distance involved is 15. Once you have the x coordinate of the endpoints, it's a simple matter to figure out the distance from the chord to the right vertex of the ellipse.

(By the way, I've been wracking by brains trying to figure out an oval that's just a stretch-out circle could be a conic section. The best I can figure is a cone with an extremely small angle, cut diagonally many miles from the apex.)

All of the conic sections arise from making slices in a cone, which by the mathematics definition, is in two parts - an upper cone portion and a lower cone portion. Away from mathematics, most people call one of these sections a "cone."

If you slice the cone perpendicular to the axis of the cone, you get a circle. If you tilt the angle at which you make the slice just a bit, you get an ellipse. Different angles generate ellipses with different major axes. If you slice the cone so that the plane of the slice is parallel to the opposite side, you get a parabola. Vertical slice, you get the two "sheets" of a hyperbola.

http://lightcolorvision.wordpress.com/
(There a diagram near the top of this blog, entitled "Need help on this problem.")

 

[zyxwv99]

Thanks, Mark44. With your help I was able to figure it out.