Question

A straight line meets the coordinate axes in $A$ and $B$. Find the equation of the straight line, when $(p,q)$ bisects $\overline{AB}$.

Answer 1

By section formula,

$p=\frac{\alpha }{2},q=\frac{\beta }{2}$

$\Rightarrow \alpha =2p,\beta =2q$

By intercept form, equation of line:

$\frac{x}{\alpha }+\frac{y}{\beta }=1$

$\Rightarrow \frac{x}{2p}+\frac{y}{2q}=1$

$\Rightarrow \frac{x}{p}+\frac{y}{q}=2$.