Trig - Converting rectangular equation to polar

Question

(x-1)^2+(y+1)^2=2 to polar

Pls help

Answer 1

Let x=r cosθ and y=r sinθ put these into the equation to get (r cosθ -1)² +( r sinθ +1)² = 2 which gives r² cos²θ -2r cosθ +1 +r² sin²θ +2 r sinθ +1 =2 r²( cos²θ +sin²θ) -2r cosθ +2r sinθ +2 =2 so r² -2r cosθ +2r sinθ =0 and r -2cosθ +2 sinθ =0.

Answer 2

Use the formulas x = rcosθ, y = rsinθ, r² = x² + y².

(x-1)² + (y+1)² = 2

x² - 2x + 1 + y² + 2y + 1 = 2

r² - 2rcosθ + 2rsinθ = 0

r = 2(cosθ - sinθ)