Question

Convert r=5/(1 +cos theta) to a rectangular equation.

Answer 1

\[r={5\over1+\cos\theta}\\
r(1+\cos\theta)=5\\
r+r\cos\theta=5
\]
we have the relation:
\[r=\sqrt{x^2+y^2}\\
x=r\cos\theta\qquad y=r\sin\theta\]
plug them in

Answer 2

\[\sqrt{x^2+y^2}+x=5\\
\sqrt{x^2+y^2}=5-x
\]
square both sides and simplify