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=0⇒x−c/a+y−c/b=1
Therefore, x−intercept =−ca and y−intercept =−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=12⇒4A=2