let T = (x,y) then
(x-cp) + p^2 (y - c/p) = 0
x + (p^2)y = 2cp
x + (q^2)y = 2cq
x = 2c / (p+q)
y = 2cpq/(p+q) = 2c / (p+q) = 2c / (p + 1/p)
so the line's x=y , x in [-c,c]
as p + 1/p >= 2 or p + 1/p <= -2
EDIT: thought about it again
if we allow p = q then it's the above line segment + 2...