Convert the polar equation to rectangular form:
r = -2cosø - 2sinø
multiply by r and you have
r^2 = -2rcosø-2rsinø
x^2+y^2 = -2x-2y
x^2+2x + y^2+2y = 0
(x+1)^2 + (y+1)^2 = 2
To convert the polar equation r = -2cosø - 2sinø to rectangular form, we can use the following relationships between polar and rectangular coordinates:
x = r*cosø
y = r*sinø
Let's substitute these values into the given polar equation:
x = -2cosø - 2sinø
y = -2cosø - 2sinø
Therefore, the rectangular form of the given polar equation r = -2cosø - 2sinø is:
x = -2cosø - 2sinø
y = -2cosø - 2sinø
Note that in this case, the polar equation and the rectangular equation are the same.