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Question

If a,c,b are in G.P. and the area formed by the coordinate axes and the line ax+by+c=0 is A sq. units, then the value of 4A is

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Solution

ax+by+c=0xc/a+yc/b=1
Therefore, xintercept =ca and yintercept =cb
So, area of the triangle,
A=12×(ca)×(cb)A=c22ab
As a,c,b are in G.P., so c2=ab
A=ab2ab=124A=2

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