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 $2x+3y+4=0$ is

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

Answer 1

Answer: (C)

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