Question

The equation of the lines parallel to $5x-12y-26=0$ and at a distance of $4units$ from it are ?

• A. $5x-12y-78=0$ & $5x-12y-26=0$
• B. $5x-12y+78=0$ & $5x-12y+26=0$
• C. $5x-12y+78=0$ & $5x-12y-26=0$
• D. None of these

Answer 1

Answer: (C)

$5x-12y+78=0$ & $5x-12y-26=0$

$5x-12y+\lambda =0$

$distancebetweentwolines\left(\frac{C_2-C_1}{\sqrt{a^2{+b}^2}}\right)$

$5x-12y+26=0$

$4=\left[\frac{\lambda -26}{\sqrt{5^2+{12}^2}}\right]=4\left[\frac{\lambda -26}{\sqrt{169}}\right]=⟨\lambda -26⟩=52;\lambda -26=52;\lambda -26=-52$

$\lambda =78\&\lambda =-26$

$5x-12y+78=0$

$5x-12y-26=0$