Question

The equation of the lines through the point $(2,3)$ and making an intercept length $2$ units between the lines $y+2x=3$ and $y+2x=5$ are

• A. $x+3=0$
• B. $y-2=0$
• C. $x-2=0$
• D. None of these

Answer 1

Answer: (C)

$x-2=0$

Given that

$\Rightarrow y+2x=3$ …….$\left(1\right)$

$\Rightarrow y+2x=5$ …….$\left(2\right)$

Put $x=0$ then by equation $\left(1\right)$ we get $y=3$ and by equation $\left(2\right)$ we get $y=5$

Hence the difference of $y$ at $x=0$ is $2$

These given lines are parallel. Therefore, the line having intercept of $2$ units will be parallel to the line $x=0$

$\Rightarrow$ Hence, the equation will be $x=c$

Given that the line passes through $(2,3)$

Therefore, $\Rightarrow c=2$

$\Rightarrow$ equation of line $\to x=2$