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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.

Answer and Explanation: 1

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We have the Cartesian equation: {eq}\displaystyle \; x^4+2 x^2 y^2+y^4- 8 x y =0 \; {/eq}.

To find the polar equation of the curve, we use the...

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Graphing Functions in Polar Coordinates: Process & Examples

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Chapter 24 / Lesson 1
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Learn how to graph polar equations and plot polar coordinates. See examples of graphing polar equations. Transform polar to rectangular coordinates and vice versa.


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