# Consider the equation in polar coordinates: r^2 = 4 What is the equation in Cartesian...

## Question:

Consider the equation in polar coordinates:

{eq}r^2 = 4 {/eq}

What is the equation in Cartesian (rectangular) coordinates equivalent to this equation in polar coordinates?

## Polar Curves

A polar curve given as {eq}\displaystyle r=f(\theta), a\leq \theta \leq b, {/eq} is converted to the Cartesian form {eq}\displaystyle g(x,y)=0 {/eq}

by using the polar-Cartesian conversion equations

{eq}\displaystyle x=r\cos \theta, y=r\sin\theta \text{ and }x^2+y^2=r^2. {/eq}

Sometimes it is easier to recognize a curve given in polar coordinates if it si converted to Cartesian coordinates.