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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

xca+ycb=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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