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

BaseAB of the triangleABC, lies along x= a

ie, lies on the line // Y axis

length of base AB = 2a

& area ( triABC) = 1/2 * 2a *altitude = a²

=> altitude = a

Hence, vertices of A,B,C as follows

Coordinates of A ( a,y )

Coordinates of B ( a, 2a-y )

Coordinates of C = ( 2a, y1 ) OR ( 0,y1)

y coordintes of these vertices can hold any value..

locus of C is either Y axis or a line parallel to Y axis