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 $\triangle OMP , \angle POM =(\theta-\alpha)$
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