If x1,x2,x3 and y1,y2,y3 are both in G.P. with the same common ratio, then the points x1,y1 x2,y2 and x3,y3
lie on an ellipse
lie on a circle
are vertices of a triangle
lie on a straight line
Let x2=x1r,x3=x1r2
y2=y1r,y3=y1r2
The given points lie on the line
x1y−y1x=0 for all values of r.