Question

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

• A. $x-2=0$
• B. $x-1=0$
• C. $2x—1=1$
• D. $x-2=2$

Answer 1

Answer: (A)

The equation of any line through the point of intersection of the given lines is of the form
$x-7y+5+k(3x+y-7)=0$
i.e. $(1+3k)x+(k-7)y+5-7k=0\dots (i)$
If this line is parallel to $y$-axis, then the coefficient of $y$ should be zero, i.e., $k-7=0$ which gives $k=7$.
Substituting this value of $k$ in the equation $(i)$,
we get $22x-44=0$,
i.e., $x-2=0$, which is the required equation.