ELLIPSE/인티그리티

 

 

ELL

 

 

 

Foci and Axes

Given the major and minor axes of an ellipse, you can always find the foci. You need the foci for some construction methods. Just draw radii of length a from the ends of the minor axis. Given the foci, however, you can't uniquely determine the axes. You need additional information such as the length of one axis. However, the major axis is always along the line through the foci and the minor axis always perpendicularly bisects the line between the foci.

Pin and String

Mostly useful as a heuristic tool to help students visualize ellipses, but it can be useful for constructing large ellipses. Put a pin in each focus and tie a string to each pin leaving slack with length 2a. Pull the string taut with a pencil point and slide the pencil to draw the ellipse. This makes use of the fact that an ellipse is the locus of points whose distances from two fixed points have a constant sum.

Trammel Method

	In my view the best method. With the major and minor axes constructed (and extended) mark a piece of paper with points O, A and B so that OA = a and AB = b. Slide O along the minor axis and B along the major axis. Point A traces out the ellipse. With any reasonable care this method is quite accurate and it is very fast.
	For cases where the axes are similar in size, the method above may be inaccurate. It is also possible to draw an ellipse using an external trammel.