question_answer

The quadratic equation whose roots are the x and y intercepts of the line passing through (1,  and making a triangle of area A with axes may be

A) \[{{x}^{2}}+Ax+2A=0\] 

B) \[{{x}^{2}}-2Ax+2A=0\]

C) \[{{x}^{2}}-Ax+2A=0\]  

D)  none of these

Correct Answer: B

Solution :

Let the equation of the line be \[\frac{x}{a}+\frac{y}{b}=1\] Area of \[\Delta POQ=\frac{1}{2}ab,\]Given \[\frac{1}{2}ab=A\Rightarrow ab=2A\] Since line (1) passes through (1, 1) \[\therefore \]\[\frac{1}{a}+\frac{1}{b}=1\]or\[a+b=ab\Rightarrow a+b=2A\] \[\therefore \]Required quadratic equation is \[{{x}^{2}}-(a+b)x+ab=0\]or\[{{x}^{2}}-2Ax+2A=0\]