Question

Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, −1).

Answer 3:

Answer 1

The equation of given line is  x + 7y + 2 = 0        ... (1)
The equation of a line parallel to line x + 7y + 2 = 0 is given below: 
$$x+7y+\lambda =0$$             ... (2)

The line  $$x+7y+\lambda =0$$  is at a unit distance from the point (1, −1).

$$\therefore 1=\left|\frac{1-7+\lambda }{\sqrt{1+49}}\right|$$
$$\Rightarrow \lambda -6=\pm 5\sqrt{2}$$
$$\Rightarrow \lambda =6+5\sqrt{2},6-5\sqrt{2}$$

Required lines :

$$x+7y+6+5\sqrt{2}=0$$ $$\text{ and }x+7y+6-5\sqrt{2}=0$$