Let k be a real parameter and consider the points A(k,0,2), B(0,k,2) and C(0,0,k) in space.
a. (i) Show that AC=BC for all real values of k, and hence identify the class of triangle ABC for arbitrary k.},{
b. (ii) Determine the value(s) of k (if any) for which △ABC is equilateral.
c. (iii) Investigate whether △ABC can ever be degenerate for any real k, and justify your answer.