The Cartesian form of the polar equation - - tan -12 is -

The correct option is A y = 2x Given polar equation is θ=tan^ 12 ⇒tanθ=2 using polar co ordiantes relation #160; x=rcosθ and y=rsinθ ...

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Standard XII

Physics

Introduction

The Cartesian...

Question

The Cartesian form of the polar equation $θ = {tan}^{- 1}$ 2 is :

x = 2 y

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y = 2 x

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x = 4 y

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y = 4 x

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Solution

The correct option is A $y = 2 x$
Given polar equation is
$θ = {tan}^{- 1} 2$
$\Rightarrow tan θ = 2$
using polar co-ordiantes relation $x = r cos θ$ and $y = r sin θ$ where $r = \sqrt{x^{2} + y^{2}}$ .
take the ratio of the above polar equation and substitute the values of $\Rightarrow tan θ = 2$
so we get ,
$\Rightarrow \frac{y}{x} = 2$
$\Rightarrow y = 2 x$

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The Cartesian form of the polar equation θ=tan−12 is :

The correct option is A y=2xGiven polar equation isθ=tan−12⇒tanθ=2using polar co-ordiantes relation x=rcosθ and y=rsinθ where r=√x2+y2.take the ratio of the above polar equation and substitute the values of ⇒tanθ=2so we get ,⇒yx=2⇒y=2x

The Cartesian form of the polar equation $θ = {tan}^{- 1}$ 2 is :