Question

If the line $6x - 7y + 8 + \lambda (3x - y + 5) = 0$ is parallel to y-axis, then $\lambda$ is equal to

• A. -7
• B. -2
• C. 7
• D. 2

Answer 1

Answer: (A)

-7

Answer 2

Given line is
$6 x-7 y+8+\lambda(3 x-y+5)=0$
$\Rightarrow (6+3 \lambda) x-(7+\lambda) y+(8+5 \lambda)=0$
$\Rightarrow (7+\lambda) y=(6+3 \lambda) x+(8+5 \lambda)$
$\Rightarrow y=\frac{3(\lambda+2)}{(\lambda+7)} x+\left(\frac{8+5 \lambda}{7+\lambda}\right)$
$\therefore$ Slope of the line $(m)=\frac{3(\lambda+2)}{(\lambda+7)}$
Since, line is parallel to $y$ -axis.
$m=\infty=\frac{1}{0}$
$\frac{3(\lambda+2)}{\lambda+7}=\frac{1}{0}$
$\Rightarrow \lambda+7=0$
$\Rightarrow \lambda=-7$