What the is the polar form of $y = y^2/x+(x-3)(y-5)$ ?

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Answer 1 · 2018-04-18T12:43:47

$r(-sinthetatantheta-rsinthetacostheta+4sintheta+5costheta)=15$

First, we expand everything to get:
$y=y^2/x+xy-3y-5y+15$

Now we need to use these:
$x=rcostheta$
$y=rsintheta$

$rsintheta=(r^2sin^2theta)/(rcostheta)+rcosthetarsintheta-3rsintheta-5rcostheta+15$

$rsintheta=rsinthetatantheta+r^2sinthetacostheta-3rsintheta-5rcostheta+15$

$rsintheta-rsinthetatantheta-r^2sinthetacostheta+3rsintheta+5rcostheta=15$

$r(-sinthetatantheta-rsinthetacostheta+4sintheta+5costheta)=15$

We cannot simplify this any further, so it stays as an implicit polar equation.

What the is the polar form of y = y^2/x+(x-3)(y-5) y = y^2/x+(x-3)(y-5) ?