Question

The angle between the lines $r\cos (\theta -\alpha )=p,r\sin (\theta -\alpha )=q$ is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\frac{5\pi }{12}$

Answer 1

Answer: (C)

$\frac{\pi }{2}$

Given $r\cos (\theta -\alpha )=p$.......(i)
$r\sin (\theta -\alpha )=q$ ...(ii)
Now, equation of line perpendicular to given line is
$r\sin (\frac{\pi }{2}+(\theta -\alpha \left)\right)=k$
$\Rightarrow r\cos (\theta -\alpha )=k$
which is of the form of given equation (i)