A line passing through the point (2,2) and the axes enclose an area λ.The intercepts on the axes made by the line are given by the two roots of
A
x2−2|λ|x+|λ|=0
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B
x2+|λ|x+3|λ|=0
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C
x2−|λ|x+2|λ|=0
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D
none of these.
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Solution
The correct option is Dx2−|λ|x+2|λ|=0 Let line is xa+yb=1 which passes through (2,2) Here, a is the x−intercept and b is the y−intercept. So 2a+2b=1 and 12ab=λ ⇒ab=2λ ∴2(a+b)ab=1⇒a+b=ab2⇒a+b=λ Product of roots is 2λ. and sum of roots is λ.