Ushbu muammoni hal qilishning turli usullari mavjud. Buning bir usuli - birinchi navbatda tenglamani qayta tartibga solish/qayta yozish.

\[\frac{2}{r} = \sin \theta - \frac{1}{{\cos \theta }}\hspace{0.5in} \to \hspace{0.5in}\frac{{2\cos \theta }}{r} = \sin \theta \cos \theta - 1\]

Ushbu nuqtada biz hamma narsani \({r^2}\) ga ko'paytirishimiz va quyidagi tarzda biroz o'zgartirishimiz mumkin:

\[2r\cos \theta = {r^2}\sin \theta \cos \theta - {r^2}\hspace{0.5in} \to \hspace{0.5in} 2r\cos \theta = \left( {r\sin \theta } \right)\left( {r\cos \theta } \right) - {r^2}\]

Endi biz ushbu muammoni hal qilish uchun quyidagi formulalardan foydalanishimiz mumkin.

\[x = r\cos \theta \hspace{0.25in}\hspace{0.25in}y = r\sin \theta \hspace{0.25in}\hspace{0.25in}{r^2} = {x^2} + {y^2}\]

Mana bu muammoning javobi,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{2x = yx - \left( {{x^2} + {y^2}} \right)}}\]