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Q.
Find the equation of line parallel to $y$-axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$.
Straight Lines
Solution:
Given, equation of lines are
$x -7 y + 5 = 0\quad ...(i)$
and $3x + y = 0 \quad ...(ii)$
On solving $(i)$ and $(ii)$, we get,
$x=\frac{-5}{22}, y=\frac{15}{22}$
Hence, the intersection point is $\left(-\frac{5}{22}, \frac{15}{22}\right)$.
$\therefore $ Equation of required line is
$y-\frac{15}{22}=\frac{1}{0}\left(x+\frac{5}{22}\right)$
$\Rightarrow 0=x+\frac{5}{22}$
$(\because$ Line is parallel to $y$-axis $\therefore m=tan\,90^{\circ}=\frac{1}{0})$
$\Rightarrow 22x + 5 = 0$