Question

The equation of the straight line, which passes through the point $(2,4)$ and makes an angle $\theta$ with positive $x$axis where $\cos \theta =-\frac{1}{3}$ is

• A. $2\sqrt{2}x-y-2\sqrt{2}+4=0$
• B. $2\sqrt{2}x+y-4\sqrt{2}-4=0$
• C. $\sqrt{2}x+y-2\sqrt{2}-4=0$
• D. $x+2\sqrt{2}y-4=0$

Answer 1

The correct option is B $2\sqrt{2}x+y-4\sqrt{2}-4=0$

We have $\cos \theta =-\frac{1}{3}(\because \frac{\pi }{2}\le \theta \le \pi )$
So, $\tan \theta =-\sqrt{8}$
Equation of line is
$y-y_1=m(x-x_1)\Rightarrow y-4=-\sqrt{8}(x-2)\Rightarrow y+\sqrt{8}x-4-2\sqrt{8}=0\Rightarrow 2\sqrt{2}x+y-4\sqrt{2}-4=0$