The Straight Lines — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 Marks
Question
Find the equation of the straight lines passing through the following pair of points: (a, b) and (a + b, a - b)
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Answer
Let $\text{A}(\text{a},\text{b})$ be $(\text{x}_1,\text{y}_1)$$\text{B}(\text{a}+\text{b},\text{a}-\text{b})$ be $(\text{x}_2\text{y}_2)$
Then equation of line AB is
$\Rightarrow \text{y}-\text{y}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)$
$\Rightarrow \text{y}-\text{b}=\frac{\text{a}-\text{b}-\text{b}}{\text{a}+\text{b}-\text{a}}(\text{x}-\text{a})$
$\Rightarrow \text{y}-\text{b}=\frac{\text{a}-\text{2b}}{\text{b}}(\text{x}-\text{a})$
$\Rightarrow\text{by}-\text{b}^2=\text{ax}-\text{a}^2-\text{2bx}+\text{2ba}$
$\Rightarrow(\text{a}-\text{2b})\text{x}-\text{by}+\text{b}^2-\text{a}^2+\text{2ab}=0$
$\therefore$ The equation of the line joining the points (a, b) and (a + b, a - b) is $(\text{a}-\text{2b})\text{x}-\text{by}+\text{b}^2-\text{a}^2+\text{2ab}=0$
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