Learn how to write a polar equation in rectangular form

The video tutorial explains the conversion between polar and rectangular coordinates, focusing on the relationships X = R cos(theta) and Y = R sin(theta). It demonstrates how to convert equations by multiplying both sides by R to create terms involving R sine and cosine. The tutorial simplifies the equation to X^2 + Y^2 = 2Y - 4X and discusses its representation. The instructor concludes by mentioning future discussions on grouping and completing the square, leaving the equation in a standard form for now.

What is the equation mentioned that relates X and Y in rectangular coordinates?

What method is suggested for simplifying equations in this context?