How do you convert the polar equation #r=2/(2-costheta)# into rectangular form?

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Answer 1 · 2016-12-14T14:04:35

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

Use the conversion formula #r(cos theta, sin theta)=(x, y)# that gives

# cos theta=x/r and r=sqrt(x^2+y^2)#.

The answer follows.

The given equation has the form

#1/r=1-1/2 cos theta#, that represents an ellipse with

eccentricity #e =1/2# and semi major axis #a = 4/3#.

Graph is inserted

graph{2sqrt(x^2+y^2)-x-2=0 [-2.5, 2.5, -1.25, 1.25]}