Question

The equations of the lines through $(1,1)$ and making angles of ${45}^{\circ }$ with the line $x+y=0$ are

• A. $x-1=0,x-y=0$
• B. $x-y=0,y-1=0$
• C. $x+y-2=0,y-1=0$
• D. $x-1=0,y-1=0$

Answer 1

Answer: (D)

$x-1=0,y-1=0$

$m=1,y-1=\frac{m\pm tan{45}^{\circ }}{1+\mp mtan{45}^{\circ }}(x-1)$,
$\Rightarrow y-1=\frac{(-1)\pm 1}{1\pm 1}(x-1)$
$\Rightarrow y=1,x=1$