How do you convert $xy=5x^2-3x+2y$ into a polar equation?

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Answer 1 · 2016-06-15T11:55:38

$r=5rtantheta-3csctheta+2sectheta$

We know that if a point in X-Y
plane has rectangular coordinate $(x,y)$ and its polar coordinate is $(r,theta)$ ,then we have the relation

$x=rcostheta and y =rsintheta$

and $r=sqrt(x^2+y^2)$

Now the given equation is

$xy=5x^2-3x+2y$

$=>rcostheta*rsintheta=5r^2sin^2theta-3rcostheta+2rsintheta$

Deviding both sides by $rsinthetacostheta$

$r=5rtantheta-3csctheta+2sectheta$

How do you convert xy=5x^2-3x+2yxy=5x^2-3x+2y into a polar equation?