How do you convert #r=1/(1-cosx)# into rectangular form?

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Answer 1 · 2018-04-22T14:12:19

The equation is #y^2=2x+1#

Apply the following to convert from polar coordinates #(r,theta)# to rectangular coordinates #(x,y)# :

#{(x=rcostheta),(y=rsintheta),(x^2+y^2=r^2), (theta=arctan(y/x)):}#

Therefore,

#r=1/(1-costheta)#

#r(1-costheta)=1#

#r-rcostheta=1#

#sqrt(x^2+y^2)-x=1#

#sqrt(x^2+y^2)=1+x#

Squaring both sides

#x^2+y^2=x^2+2x+1#

#y^2=2x+1#

graph{y^2-2x-1=0 [-8.89, 8.89, -4.444, 4.445]}