If a, c, b are in G.P , then the area of the triangle formed by the lines  ax+by+c=0 with the coordinates axes is equal to

ax-c+by-c=1x-ca+y-cb=1Area of the triangle =12 (x intercept) ×  (y intercept)=12(−ca)(−cb)=12c2ab=12[∵ a, c, b are in G.P ⇒c2=ab ]