Question

$\frac{x-x_1}{\cos \theta }=\frac{y-y_1}{\sin \theta }=r$, represents:

• A. Equation of straight line, if $\theta$ is variable & $r$ is constant
• B. Equation of circle, if $r$ is variable & $\theta$ is constant
• C. Equation of circle, if $\theta$ is variable & $r$ is constant
• D. Equation of straight line, if $r$ is variable & $\theta$ is constant

Answer 1

Answer: (C), (D)

The correct options are
C Equation of circle, if $\theta$ is variable & $r$ is constant
D Equation of straight line, if $r$ is variable & $\theta$ is constant

If $r$ is variable and $\theta$ is constant,
then $\frac{x-x_1}{\cos \theta }=\frac{y-y_1}{\sin \theta }=r$, represents parametric form of a line -----------(2)

From(1) and (2), Option C and option D are correct.