Question

The equations of the lines which cuts off an intercept $-1$ from $y$ -axis and equally inclined to the axes are

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

Answer 1

Answer: (C)

Here, $c =-1$ and $m =\tan \,\theta=\tan\, 45^{\circ}=1$
(Since the line is equally inclined to the axes, so $\theta=45^{\circ}$ )
Also, $m =\tan 135^{\circ}=-1 $
$\Rightarrow m =\pm 1$
$\therefore \theta=45^{\circ}$ and $135^{\circ}$
Hence, equation of straight line is
$y =\pm(1 \cdot x )-1$
$\Rightarrow x-y-1=0$ and $x+y+1=0$