(x+1)^2+y^2=1 convert equation from rectangular to polar form

The polar form of the equation is -2 cosθ

Explanation:

( x + 1 )² + y² = 1

r² = x² + y²

Use x = r cosθ and y = r sinθ

Substitute these variable in x and y

( r cosθ + 1 )² + ( r sinθ )² = 1²

r² cos²θ + 1 + 2 r cosθ + r² sin²θ = 1

r² ( cos²θ + sin²θ ) + 1 + 2 r cosθ = 1

r² + 1 + 2 r cosθ = 1

r² + 2 r cosθ = 0

r² = -2 r cosθ

r = -2 cosθ

Therefore, the polar form of the equation is -2 cosθ

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