Solve r = 4 - 4 cos(\theta )

Evaluate

r = 4 - 4 cos (θ)

Multiply both sides

r^{2} = 4 r - 4 cos (θ) \times r

Rewrite the expression

4 cos (θ) \times r + r^{2} - 4 r = 0

Use substitution

More Steps

4 x + x^{2} + y^{2} - 4 r = 0

Simplify the expression

- 4 r = - 4 x - x^{2} - y^{2}

Square both sides of the equation

(- 4 r)^{2} = (- 4 x - x^{2} - y^{2})^{2}

Evaluate

16 r^{2} = (- 4 x - x^{2} - y^{2})^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

16 (x^{2} + y^{2}) = (- 4 x - x^{2} - y^{2})^{2}

Evaluate the power

16 (x^{2} + y^{2}) = (4 x + x^{2} + y^{2})^{2}

Calculate

16 x^{2} + 16 y^{2} = 16 x^{2} + x^{4} + y^{4} + 8 x^{3} + 8 x y^{2} + 2 x^{2} y^{2}

Move the expression to the left side

16 x^{2} + 16 y^{2} - 16 x^{2} = x^{4} + y^{4} + 8 x^{3} + 8 x y^{2} + 2 x^{2} y^{2}

Calculate

0 + 16 y^{2} = x^{4} + y^{4} + 8 x^{3} + 8 x y^{2} + 2 x^{2} y^{2}

Solution

16 y^{2} = x^{4} + y^{4} + 8 x^{3} + 8 x y^{2} + 2 x^{2} y^{2}

Function