Q. Lines are drawn parallel to the line $4x - 3y + 2 = 0$, at a distance $\frac{3}{5}$ from the origin. Then which one of the following points lies on any of these lines ?
Solution:
Required line is $4x - 3y + \lambda = 0$
$ \left| \frac{\lambda}{5} \right| = \frac{3}{5}$
$\Rightarrow \; \lambda = \pm 3 .$
So, required equation of line is $4x - 3y + 3 = 0$ and $4x - 3y - 3 = 0$
$(1) \, 4\left( - \frac{1}{4}\right) - 3 \left(\frac{2}{3}\right) + 3 = 0 $
