A line passes through P(1,2) such that its intercept between the axes is bisected at P. Find the equantion of the line.

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$$\begin{gathered} \mathrm{Let} \mathrm{X}-\mathrm{axis} \mathrm{intercept} \mathrm{of} \mathrm{line} \mathrm{be} \mathrm{A}\left(\mathrm{a},0\right) \mathrm{and} \mathrm{Y}-\mathrm{axis} \mathrm{intercept} \mathrm{of} \mathrm{line} \mathrm{be} \left(0,\mathrm{b}\right). \\ \mathrm{Hence} \mathrm{equation} \mathrm{of} \mathrm{line} \mathrm{will} \mathrm{be}: \\ \frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1 \\ \mathrm{According} \mathrm{to} \mathrm{question} \mathrm{P}\left(1,2\right) \mathrm{is} \mathrm{mid} \mathrm{point} \mathrm{of} \mathrm{A}\left(\mathrm{a},0\right) \mathrm{and} \mathrm{B}\left(0,\mathrm{b}\right) \\ \Rightarrow \frac{\mathrm{a}+0}{2}=1 \mathrm{and} \frac{0+\mathrm{b}}{2}=2 \\ \Rightarrow \mathrm{a}=2 \mathrm{and} \mathrm{b}=4 \\ \mathrm{Hence} \mathrm{equation} \mathrm{of} \mathrm{line} \mathrm{will} \mathrm{be}: \\ \frac{\mathrm{x}}{2}+\frac{\mathrm{y}}{4}=1 \\ \mathrm{Multiplying} \mathrm{each} \mathrm{term} \mathrm{by} 4 \mathrm{we} \mathrm{get}: \\ 2\mathrm{x}+\mathrm{y}=4 \\ \Rightarrow \boxed{\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{-}\mathbf{4}\mathbf{=}\mathbf{0}} \end{gathered}$$

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