⇒OB=OC=a
So, the coordinates of point B are (0,a) and the coordinates of C are (0,−a)
We know that the line joining a vertex of an equilateral triangle with the mid-point of its opposite side is perpendicular.
Hence, vertex A lies on x-axis.
So, let the coordinates of point A be (x,0)
On applying Pythagoras theorem △ABC, we get
(AC)2=(OA)2+(OC)2
⇒(2a)2=x2+a2
⇒4a2−a2=x2
⇒x2=3a2
⇒x=±√3a
∴ coordinates of point A are (±√3a,0) or (−√3a,0)
Thus, the vertices of the given equilateral triangle are (0,a)(0,−a) and (√3a,0) or (0,a)(0,−a) and (−√3a,0)