r=$\displaystyle sec^2{\theta\over 2}$
Book answer is: $\displaystyle y^2=-4x+4$
How is it that you arrived at the answer? I've tried many ways and am no closer to the answer than when I started, please help.
Maybe there is an easier way, but... First express $\displaystyle \sec^2(\theta/2)$ through $\displaystyle \cos\theta$ using the double-angle formula. Then replace r by $\displaystyle \sqrt{x^2+y^2}$ and $\displaystyle \cos\theta$ by $\displaystyle x/\sqrt{x^2+y^2}$ and simplify. It may be necessary to separately check special cases, such as when r = 0.
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