Question

# 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.

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Solution

## 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

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