# Convert the Cartesian equation {eq}x^{4}+2 x^{2} y^{2}+y^{4}=8 x y {/eq} to a polar equation.

## Question:

Convert the Cartesian equation {eq}x^{4}+2 x^{2} y^{2}+y^{4}=8 x y {/eq} to a polar equation.

## Polar Coordinates:

We have the Cartesian equation of a curve in the shape of infinity (a figure eight) in the plane. We can find the polar equation of this curve by using the transformation equations between Cartesian and polar coordinates. The resulting equation can be simplified by using trigonometric identities.