How do you convert r = 1/(8 - cos(theta)) into rectangular form?

1 Answer
Alan P.
Dec 7, 2015

8sqrt(x^2+y^2)-x=1

Explanation:

In converting between polar and rectangular forms:
color(white)("XXX")r=sqrt(x^2+y^2)
and
color(white)("XXX")cos(theta)=x/r = x/(sqrt(x^2+y^2))

Therefore, given
color(white)("XXX")r = 1/(8-cos(theta))

We have
color(white)("XXX")r = 1/(8-x/r)

color(white)("XXX")r= 1/((8r-x)/r)

color(white)("XXX")r= r/(8r-x)

color(white)("XXX")8r-x=1

color(white)("XXX")8(sqrt(x^2+y^2))-x = 1

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