How do you convert the polar equation $r=6/(2costheta-3sintheta)$ into rectangular form?

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Answer 1 · 2017-01-22T09:51:52

The equation is $y=2/3x-2$

To convert from polar coordinates $(r, theta)$ to rectangular coordinates $(x,y)$ , we use the equations

$x=rcostheta$

$y=rsintheta$

Let's rewrite the equation

$r=6/(2costheta-3sintheta)$

$r(2costheta-3sintheta)=6$

$2rcostheta-3rsintheta=6$

Therefore,

$2x-3y=6$

$3y=2x-6$

$y=2/3x-2$

This is the equation of a line

How do you convert the polar equation r=6/(2costheta-3sintheta)r=6/(2costheta-3sintheta) into rectangular form?