Exercise 25.  Let   and   be two distinct points in the complex plane, and let  K  be a positive real constant that is greater than the distance between   and   .

25 (a).  Show that the set of points    is an ellipse with foci   and .  

Solution 25 (a).

See text and/or instructor's solution manual.

By definition, an ellipse is the locus of points the sum of whose distances from two fixed points is constant.  

Since gives the distance from the point z to the point ,  and gives the distance from the point z to the point ,  the set    is precisely those points that satisfy the definition of an ellipse.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell