Question

A line meets x–axis and y-axis at the points A and B respectively. If the middle point of AB be $\left( x _ { 1 } , y _ { 1 } \right)$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. $x _ { 1 } x + y _ { 1 } y = x _ { 1 } y _ { 1 }$

Answer 1

Answer: (A)

$y _ { 1 } x + x _ { 1 } y = 2 x _ { 1 } y _ { 1 }$

Answer 2

Obviously, $x _ { 1 } = \frac { a } { 2 }$and $y _ { 1 } = \frac { b } { 2 }$.

Therefore the equation of line $A B$ is

$\frac { x } { a } + \frac { y } { b } = 1$

⇒ $\frac { x } { 2 x _ { 1 } } + \frac { y } { 2 y _ { 1 } } = 1 \Rightarrow x y _ { 1 } + y x _ { 1 } = 2 x _ { 1 } y _ { 1 }$.