How do you convert the polar equation $r = \frac{5}{4 cos θ - 2 sin θ}$ $r=5/(4costheta-2sintheta)$ into rectangular form?

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Answer 1 · 2016-10-28T14:10:57

$4 x - 2 y = 5$ $4x-2y=5$

The relation between polar coordinated $(r, θ)$ $(r,theta)$ and Cartesian rectangular coordinates $(x, y)$ $(x,y)$ is given by

$x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$

Hence $r = \frac{5}{4 cos θ - 2 sin θ}$ $r=5/(4costheta-2sintheta)$

$\Leftrightarrow 4 r cos θ - 2 r sin θ = 5$ $hArr4rcostheta-2rsintheta=5$

or $4 x - 2 y = 5$ $4x-2y=5$

How do you convert the polar equation r=5/(4costheta-2sintheta)r=54cosθ−2sinθr=5/(4costheta-2sintheta) into rectangular form?