What the is the polar form of #y = y/x+(x+2)(y+1) #?

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Answer 1 · 2017-12-02T13:52:16

#sintheta+r^2cos^2thetasintheta+rcos^2theta+1/2rsin2theta+2costheta=0#

We use the fact that:

#x=rcostheta# and #y=rsintheta#.

These can be substituted into the equation.

First expand the brackets of.

#y=y/x+(x+2)(y+1)#

#y=y/x+xy+x+2y+2#

Substituting:

#rsintheta=(rsintheta)/(rcostheta)+rcosthetarsintheta+rcostheta+2rsintheta+2#

Simplify:

#0=sintheta+r^2cos^2thetasintheta+rcos^2theta+1/2rsin2theta+2costheta#