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)

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