question_answer

A line meets x?axis and y-axis at the points A and B respectively. If the middle point of AB be \[({{x}_{1}},\ {{y}_{1}}),\]then the equation of the line is

A)            \[{{y}_{1}}x+{{x}_{1}}y=2{{x}_{1}}{{y}_{1}}\]

B)            \[{{x}_{1}}x+{{y}_{1}}y=2{{x}_{1}}{{y}_{1}}\]

C)            \[{{y}_{1}}x+{{x}_{1}}y={{x}_{1}}{{y}_{1}}\]             

D)            \[{{x}_{1}}x+{{y}_{1}}y={{x}_{1}}{{y}_{1}}\]

Correct Answer: A

Solution :

           Obviously, \[{{x}_{1}}=\frac{a}{2}\]and \[{{y}_{1}}=\frac{b}{2}\].            Therefore the equation of line \[AB\] is \[\frac{x}{a}+\frac{y}{b}=1\]                    Þ  \[\frac{x}{2{{x}_{1}}}+\frac{y}{2{{y}_{1}}}=1\Rightarrow x{{y}_{1}}+y{{x}_{1}}=2{{x}_{1}}{{y}_{1}}\].