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 $x+y+1=0$