Question

Find the equation of line parallel to $y$-axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$.

• A. $x + 22 = 0$
• B. $22x + 5 = 0$
• C. $x +44 = 0$
• D. $22x - 5 = 0$

Answer 1

Answer: (B)

$22x + 5 = 0$

Answer 2

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 $\therefore m=tan\,90^{\circ}=\frac{1}{0})$ $\Rightarrow 22x + 5 = 0$