Question

The equation of the straight line passing through the origin and the middle point of the portion of the line ax + by + c = 0 between the axes, is

• A. ax + by = 0
• B. ax – by = 0
• C. bx + ay = 0
• D. bx – ay = 0

Answer 1

The correct option is B

ax – by = 0

The equation of the given line is ax + by + c = 0

$\Rightarrow ax+by=-c\Rightarrow \frac{x}{\frac{-c}{a}}+\frac{y}{-c/b}=1$ .......(1)

Let the line (1) cuts x-axis and y-axis at the points A and B respectively, then

$A\equiv (-\frac{c}{a},0)andB\equiv (0,-\frac{c}{b})$

The coordinates of the middle point C of AB are

$(\frac{\frac{-c}{a}}{2},\frac{0-\frac{c}{b}}{2})or(-\frac{c}{2a},-\frac{c}{2b})$

Now, equation of the line OC is

$y-0=\frac{\frac{c}{2b}}{\frac{c}{2a}}(x-0)ory=\frac{a}{b}\times orax-by=0$