Question

Obtain the equation of the line passing through the intersection of the lines $2x-3y+4=0$ and $3x+4y=5$, and drawn parallel to $y$-axis.

• A. $20x+1=0$
• B. $17x+1=0$
• C. $10x+1=0$
• D. $2x+1=0$

Answer 1

Answer: (B)

Any line through the intersection of $2x-3y+4=0$ and $3x+4y-5=0$ can be taken as
$2x-3y+4+k(3x+4y-5)=0$
or $x(2+3k)+y(4k-3)+4-5k=0\dots (i)$
This line is parallel to $y$-axis if $4k-3=0$ i.e., if $k=\frac{3}{4}$.
Substituting $k=\frac{3}{4}$ in $\left(i\right)$, we get
$x\left(2+\frac{9}{4}\right)+y\left(3-3\right)+4-\frac{15}{4}=0$,
i.e., $17x+1=0$