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

Question

1065 views around the world

You can reuse this answer
Creative Commons License

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.