If a, b, c are in G.P. write the area of the triangle formed by the line ax+by+c=0 with the coordinates axes.
a,b,c are in G.P.
⇒b2=ac ...(1)
Given lines is,
ax+by+c=0
ax+by=−c
x−ca+y−cb=1
Thus,intercept by line on x axis is -ca
and on y-axis is -cb
Area of Δ=12 (−ca)(−cb)
=12(c2ab)
=12(b2a2ab) [Using (1)]
Area of Δ=12(ba)3 sq.units