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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 (3, 4) and is such that the portion of it intercepted between the axes is divided by the point in the ratio 2 : 3.
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Answer

Suppose P = (3, 4) divides the line joining the points A(a, 0) and B(0, b) in the ratio 2 : 3.Then,
$3=\frac{2(0)+3(\text{a})}{2+3}\Rightarrow3=\frac{3\text{a}}{5}\Rightarrow\text{a}=5$
$4=\frac{2(\text{b})+3(0)}{2+3}\Rightarrow4=\frac{2\text{b}}{5}\Rightarrow\text{b}=10$
$\therefore$ A is (5, 0), B is (0, 10)
Equation of AB is
$\frac{\text{x}}{5}+\frac{\text{y}}{10}=1$
$\text{2x}=\text{y}=10$

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