Solve r^2=4r^3 - ScanMath

Evaluate

r^{2} = 4 r^{3}

Rewrite the expression

r^{2} - 4 r^{3} = 0

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

x^{2} + y^{2} - 4 r^{3} = 0

Simplify the expression

- 4 r^{3} = - x^{2} - y^{2}

Evaluate

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

Evaluate

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

Square both sides of the equation

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

Evaluate

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

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

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

Use substitution

(16 x^{4} + 32 x^{2} y^{2} + 16 y^{4}) (x^{2} + y^{2}) = (- x^{2} - y^{2})^{2}

Evaluate the power

(16 x^{4} + 32 x^{2} y^{2} + 16 y^{4}) (x^{2} + y^{2}) = (x^{2} + y^{2})^{2}

Solution

16 x^{6} + 48 x^{4} y^{2} + 48 x^{2} y^{4} + 16 y^{6} = x^{4} + 2 x^{2} y^{2} + y^{4}

Solve the equation