Ellipse Fun (More to Come Soon)

Intro: Why Ellipses Are Cool!

Ellipse Constructions and Interpretations

The Thumbtack Drawing Construction

Challenge 1

Figure out what the relationship between the length of the major axis, given by 2a, and the length of the string, L

Hint:

Examine the geometry of the string in the interactive above by looking at the condition in which the red dot is at the top center point (x=0) and the condition in which the red dot is at the rightmost point (x=a).

Challenge 2

Given the length of the string, L, and the distance between foci, given by 2c in the above diagram, find the length of semi-minor axis, b. Alternatively, given a and b, find the distance between the foci, given by 2c.