The cartesian form of the polar equation $\theta=\tan ^{-1} 2$ is

• A

  $x=2 y$
• Correct answer
  B

  $y=2 x$
• C

  $x=4 y$
• D

  $y=4 x$

Solution

Given that
$\begin{aligned} & \theta=\tan ^{-1} 2 \\ & \Rightarrow \quad \tan \theta=2 \\ & \text { We know, } x=r \cos \theta, y=r \sin \theta \\ & \Rightarrow \quad \tan \theta=\frac{y}{x} \\ & \therefore \quad y=2 x \\ & \end{aligned}$

Hence, the correct answer is option: 'B'.