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The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 Marks
Question
Find the equation of the line which passes through the point (-4, 3) and is such that the portion of it between the axes is divivded by the point in the ratio 5 : 3.
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Answer

Let equation of line be $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$It is given (-4, 3)divides the line joining A(a, 0) and B(0, b)in ratio 5 : 3
$\therefore\Big(\frac{3\text{a}}{8},\frac{5\text{b}}{8}\Big)=(-4,3)$
$\Rightarrow\frac{3\text{a}}{8}=-4\ \Rightarrow\text{a}=\frac{-32}{3}$
And
$\frac{5\text{b}}{8}=3\ \Rightarrow\text{b}=\frac{24}{5}$
$\therefore$ The equation of line is
$\frac{3\text{x}}{-32}+\frac{\text{5y}}{24}=1$
or $\text{9x}-\text{20y}+96=0$

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