Question

A straight line parallel to the lines $3x-y-3=0$ and $3x-y-5=0$ and lies between them. If its distance from these lines are in the ratio $3:5$ then its equation will be

• A. $3x-y+1=0$
• B. $3x-y+2=0$
• C. $3x-y=0$
• D. None of these

Answer 1

Answer: (C)

$3x-y=0$

$GivenLines:$

$3x-y-3=0$

Distance from the origin $d_1=\frac{|-3|}{\sqrt{3^2+1}}=\frac{3}{\sqrt{10}}$

$3x-y-5=0$

Distance from the origin $d_2=\frac{|-5|}{\sqrt{3^2+1}}=\frac{5}{\sqrt{10}}$

Let the equation of third line be $3x-y=\lambda$ ......(1)

$\frac{d_1}{d_2}=\frac{3}{5}$ which is the ratio in which required line must divide the given lines.

Hence, equation (1) must pass through the origin

$0-0=\lambda or\lambda =0$

So, the line $3x-y=0$ is parallel to the lines $3x-y-3=0$ and $3x-y-5=0.$