The base of the triangle lies along the line x=a and is of length a. The area of the triangle is a2.The locus of the third vertex is

The vertices lying on the line x= a are →
(a,b)  (a, a+b) where b is distnce from x – axis on that line reapextively.
Let the 3^rd vrtx be (h,k).

the area =>> a^2 =   |h   k   1|
                           |a a+b 1|
                           |a   b   1|
therefore, 
h(a) – a^2 = a^2
ah -2a^2 =0
a(h-2a) =0
a cannot be zero therfore,
h – 2a = 0
or
x = 2a is locus of the third vertex.