Question

If a line is parallel to $3x+4y-12=0$ is at a distance of $2$ units from a fixed point $(6,0)$, then the equation of line is/are

• A. $3x+4y-8=0$
• B. $3x+4y-18=0$
• C. $3x+4y-28=0$
• D. $3x+4y-38=0$

Answer 1

Answer: (A), (C)

The correct options are
A $3x+4y-8=0$
C $3x+4y-28=0$

Required line equation is
$3x+4y+k=0$

Distance from $(6,0)$ is $2$ units
$\therefore \frac{|3\left(6\right)+4\left(0\right)+k|}{5}=2$
$\Rightarrow 18+k=\pm 10\Rightarrow k=-8\text{or}-28$

$\therefore$ Required line equations are
$3x+4y-8=0$ and $3x+4y-28=0$