SOLUTION: Find an equation of the set of points on a plane such that the sum of the distances between each point of the set and the points (0,3) and (0,-3) is 10 units.

This set of points is the ellipse on a coordinate plane, centered at the origin

and having focuses at given points (0,3)  and  (0,-3).


Its major axis is vertical; minor axis is horizontal;


the major semi-axis "a" has the length 

    (a-3) + (a-(-3)) =10,  or, equivalently,  (a-3) + (a+3) = 10,  2a = 10,  a = 5 units.


The minor semi-axis "b" has the length  b =  =  =  = 4 units.


The canonical equation of this ellipse is


     +  = 1.      ANSWER