Question

Let $P(x,y)$ be the Cartesian coordinates with respect to axes $OX$ and $OY$, then $(r,\theta )$ be its polar coordinates with respect to pole $O$ and initial line $OX$ i.e., $OP=r$ (radius vector) and $\angle XOP=\theta$ (vectorial angle) Now let $p$ be the length of perpendicular from $O$ upon straight line (through $A,B$ ) i.e., $OM=p$ and $\angle XOM=\alpha$

In $△OMP,\angle POM=(\theta -\alpha )$
We have, $OM=OP\cos (\theta -\alpha )$
or $p=r\cos (\theta -\alpha )$ which is the required equation to the given line.
If $\frac{\ell }{r}=f(\theta )$, where $f(\theta )=a\cos (\theta +\alpha )+b\cos (\theta +\beta )$, represents a straight line then any line perpendicular to it is-

• A. $\frac{\ell }{r}=J(\theta +\pi /2)$
• B. $\frac{\ell }{r}=f(\theta +\pi /2)$
• C. $\frac{\lambda }{r}=J(\theta +\pi /2)$, where $\lambda$ is a parameter
• D. $\frac{\lambda }{r}=f(\theta +\pi /2)$, where $\lambda$ is a parameter

Answer 1

Answer: (C)

Correct answer is (c) $\frac{\lambda }{r}=J(\theta +\pi /2)$, where $\lambda$ is a parameter