Question

If a straight line passes through the point $(\alpha ,\beta )$ and the portion of the line intercepted between the axes is divided equally at that point, then $\frac{x}{\alpha }+\frac{y}{\beta }$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (C)

$2$

Let the line be $AB=\frac{x}{a}+\frac{y}{b}=1$
$\therefore$ The coordinates of $A$ and $B$ are respectively $(a,0)$ and $(0,b)$
Since, $(\alpha ,\beta )$ is the mid-point of $AB$
$\therefore \alpha =\frac{a}{2},\beta =\frac{b}{2}$

$\therefore a=2\alpha$ and $b=2\beta$

$\therefore$ From Eq. (i), $\frac{x}{2\alpha }+\frac{y}{2\beta }=1\Rightarrow \frac{x}{\alpha }+\frac{y}{\beta }=2$