Question 1086405
<pre><font size = 4><b>
{{{drawing(400,300,-8,8,-6,6, 
green(line(-7,0,7,0)), locate(-6,0,x),locate(6,0,x),
arc(0,0,14,2sqrt(24)), circle(-5,0,.1), circle(5,0,.1),
locate(-7.2,-.1,P),locate(-5,-.1,Q),locate(5,-.1,R),locate(7.1,-.1,S))}}}

The vertices are P and S
The foci are Q and R

Given: QR = 2c
       PS = 2a

To find: PQ = RS = x

     PS = PQ + QR + RS

     2a =  x + 2c +  x

     2a = 2x + 2c

2a - 2c = 2x

  a - c = x

Answer: a - c

Edwin</pre></font></b>