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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 $\frac{x}{a}+\frac{y}{\beta}$ is
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Let the line be $A B=\frac{x}{a}+\frac{y}{b}=1$
$\ldots(0$
$\therefore$ The coordinates of $A$ and $B$ are respectively
$(a, 0)$ and $(0, b)$
Since, $(\alpha, \beta)$ is the mid-point of $A B$
$\begin{array}{ll}\therefore \quad & \alpha=\frac{a}{2}, \beta=\frac{b}{2} \\ \therefore & a=2 x \text { and } b=2 \beta\end{array}$
Crom Eq. (i), $\frac{x}{2 x}+\frac{y}{2 \beta}=1 \Rightarrow \frac{x}{\alpha}+\frac{y}{\beta}=2$
$\ldots(0$
$\therefore$ The coordinates of $A$ and $B$ are respectively
$(a, 0)$ and $(0, b)$
Since, $(\alpha, \beta)$ is the mid-point of $A B$
$\begin{array}{ll}\therefore \quad & \alpha=\frac{a}{2}, \beta=\frac{b}{2} \\ \therefore & a=2 x \text { and } b=2 \beta\end{array}$
Crom Eq. (i), $\frac{x}{2 x}+\frac{y}{2 \beta}=1 \Rightarrow \frac{x}{\alpha}+\frac{y}{\beta}=2$
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