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Solve the given problems: sketch or display the indicated curves. In order to display the graph of the rectangular equation $4\left(x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4...

Question

Solve the given problems: sketch or display the indicated curves. In order to display the graph of the rectangular equation $4\left(x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}-x^{4}-2 x^{2} y^{2}-y^{4}\right)+y^{2}=0$ on a computer screen, it is first transformed into polar coordinates. Transform the equation and then sketch the graph. (Hint: the equation can be written as $4\left(x^{2}+y^{2}\right)^{3}-4\left(x^{2}+y^{2}\right)^{2}+y^{2}=0$.

Solve the given problems: sketch or display the indicated curves. In order to display the graph of the rectangular equation $4\left(x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}-x^{4}-2 x^{2} y^{2}-y^{4}\right)+y^{2}=0$ on a computer screen, it is first transformed into polar coordinates. Transform the equation and then sketch the graph. (Hint: the equation can be written as $4\left(x^{2}+y^{2}\right)^{3}-4\left(x^{2}+y^{2}\right)^{2}+y^{2}=0$.



Answers

Find a polar equation for the curve represented by the given Cartesian equation.

$ x^2 - y^2 = 4 $


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