Question

The equation of a straight line which passes through the point $(2,1)$ and makes an angle of $\pi / 4$ with the straight line $2 x+3 y+4=0$ is

• A. $x+5 y+3=0$
• B. $x-5 y+1=0$
• C. $5 x+y-11=0$
• D. $5 x-y+1=0$

Answer 1

Answer: (C)

Let slope of required line is $m$
Now, $ y-1=m(x-2)$
$\tan 45^{\circ}=\left|\frac{m+\frac{2}{3}}{1-\frac{2 m}{3}}\right|=\left|\frac{3 m+2}{3-2 m}\right|$
$\Rightarrow \frac{3 m+2}{3-2 m}=\pm 1 \Rightarrow 3 m+2=\pm(3-2 m)$
$\Rightarrow m =1 / 5,-5 $
Hence, $y - 1 =\frac{1}{5}(x-5) \Rightarrow x - 5y + 3 =0$
$y-1=-5(x-2) \Rightarrow 5 x+y-11=0 $