Question

If two lines are intersecting at $(4,3)$ and angle between them is ${45}^{\circ }$. If the slope of one line is $2$, then the equation(s) of other line is/are

• A. $3x-y-9=0$
• B. $3x+y-15=0$
• C. $x-3y+5=0$
• D. $x+3y-13=0$

Answer 1

Answer: (B), (C)

$x-3y+5=0$

Let slope of required line $=m$
$\Rightarrow \tan {45}^{\circ }=\left|\frac{m-2}{1+2m}\right|$
$\Rightarrow 1=\left|\frac{m-2}{1+2m}\right|$
$\Rightarrow 1+2m=\pm (m-2)$
$\Rightarrow m=-3,1/3$
Now this lines passes through $(4,3)$,then the equations of lines are :
$y-3=-3(x-4),y-3=\frac{1}{3}(x-4)$
$\Rightarrow 3x+y-15=0,x-3y+5=0$