SOLUTION: A landscaper wishes to create an elliptical garden at 12 m long and 4 m across with decorative fountains at the foci. How far apart are the fountains?

Draw in an xy-coordinate system with the origin at the center:



The distance from the center to the vertex = a =  the distance 
between the vertices =  the length of the major axis = 12m = 6m

The distance from the center to the covertex = b =  the distance 
between the covertices =  the length of the minor axis = 4m = 2m

c = the distance between the center and a focus.  
So the distance between the foci is 2c



For any ellipse,

c² = a² - b²
c² = 6² - 2²
c² = 36 - 4
c² = 32
 c = √32
 c = √16·2
 c = 4·√2

So 2c = 2(4·√2) = 8·√2 m.

2c = 8·(1.732) = 11.3 meters approximately  

Edwin