Convert Equation from Rectangular to Polar Form

Problems were equations in rectangular form are converted to polar form, using the relationship between polar and rectangular coordinates, are presented along with detailed solutions.
In what follows the polar coordinates of a point are (R , t) where R is the radial coordinate and t is the angular coordinate.
The relationships between the rectangualr (x,y) and polar (R,t) coordinates of a points are given by
R 2 = x 2 + y 2       y = R sin t       x = R cos t

Problems on Converting Rectangualar Equations to polar form

Problem 1

Convert the equation
2x 2 + 2y 2 - x + y = 0

to polar form.

Solution to Problem 1

Problem 2

Convert the equation
x + y = 0

to polar form.
Solution to Problem 2

More References and Links to Polar Coordinates and Trigonometry

Polar Coordinates.