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The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 Marks
Question
If the straight line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ passes through the point of intersection of the lines $x + y = 3$ and $2x - 3y = 1$ and is parallel to $x - y - 6 = 0$, find a and b.
✓

Answer

If point of intersection of lines $x+y=3$ and $2 x-3 y=1$ is $x=3-y 2(3-y)-3 y=16-2 y-3 y=1-5 y=-5 y=1 \Rightarrow$ $x=3-1=2 $
$\therefore$ Point is $(2,1)$ Any line parallel to $x-y-6=0$ Will have the same slope $=1$
$\therefore$ Equation of line parring through $(2,1)$ and having slope $=1$ is $y-y_1=m\left(x-x_1\right) y-1=1(x-2) y-1=x-2 y-x=-2+1 y-x=-1 x-y=1$ $\therefore a=1, b=-1\left(\right.$ Comparring with $\left.\frac{x}{a}+\frac{y}{b}=1\right)$

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