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The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines2 Marks
Question
Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
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Answer

The equation of the given line is,$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$
It cuts the axes at A(a, 0) and B(0, b)
THe portion of AB intercepted between the axis is 5 : 3.
$\therefore\text{h}=\frac{3\times\text{a}+5\times0}{8}$ and $\text{k}=\frac{3\times0+5\times\text{b}}{8}$
$\Rightarrow\text{p}=\Big(\frac{3\text{a}}{8},\frac{5\text{b}}{8}\Big)$
The line is passing through the point (-4, 3)
$\Rightarrow\frac{3\text{a}}{8}=-4\ \frac{5\text{b}}{8}=3$
$\Rightarrow\text{a}=\frac{-32}{3}\ \text{b}=\frac{24}{5}$
$\therefore$ The equation of the given line is,
$\frac{\text{x}}{\frac{-32}{3}}+\frac{\text{y}}{\frac{24}{5}}=1$
$\frac{-3\text{x}}{32}+\frac{\text{5y}}{24}=1$
$\text{9x}-\text{20y}+96=0$

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