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

{eq}\displaystyle 4 y^2 = x {/eq}

Question:

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

{eq}\displaystyle 4 y^2 = x {/eq}

Cartesian to Polar Equation:


The relation between polar and Cartesian coordinates is given as: {eq}x = r\cos \theta {/eq} and {eq}y = r\sin \theta {/eq}

Here, {eq}r {/eq} is the radius and {eq}\theta {/eq} is the angle.

To convert a Cartesian equation into a polar equation, substitute {eq}x = r\cos \theta {/eq} and {eq}y = r\sin \theta {/eq}.


Answer and Explanation: 1

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Given:


  • The Cartesian equation is {eq}4{y^2} = x {/eq}.


Substitute {eq}x = r\cos \theta {/eq} and {eq}y = r\sin \theta {/eq} to obtain 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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