# 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}.

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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...