The equation in rectangular coordinates. (x - 1)² + y² = 1
There are many types of coordinate system depending upon the usage and ease of working , Spherical , Rectangular , Cylindrical , Polar are the examples of Coordinate System.
It is given that the equation in polar coordinates is r = 2 cosθ
To change in rectangular coordinates
The relation between polar and rectangular coordinate is
x = r cosθ and y = r sinθ
x² + y² = r²
r = 2 cosθ
r² = 2r cosθ
r² = x
so the equation in rectangular coordinate system becomes
x² + y² = 2x
x² - 2x + y² = 0
x² - 2x + 1 + y² - 1 = 0
(x - 1)² + y² = 1
This represents the equation in rectangular coordinates.
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