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# Circles in Polar Form

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In this lesson, we will learn about circles in polar form. First, we will learn about the easiest scenario, which is a circle whose center is at the origin. For this case, we will find a polar equation of the form r = a. This tells us no matter what the angle, from the pole we can walk forward by a units and place a point. We can then connect the points with a circle. Afterwards, we will move into the harder scenario where our circle is not centered at the origin. We will derive a formula using the law of cosines that allows us to write a general formula for the equation of a circle in polar form. From there, we will learn about some special case scenarios that occur when our circle passes through the origin. When this occurs, we will be able to use a formula based on the given situation to quickly convert between polar and rectangular forms of the circle.

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