Problem

A circle is represented by the polar equation r=3cos⁡(θ). What is the center and the radius of this circle?

Answer

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Answer

Step 3: The center of the circle in polar coordinates is always (0,0) for equations of the form r=Rcos⁡(θ) or r=Rsin⁡(θ). So, the center of this circle is (0,0).

Steps

Step 1 ：Step 1: Recognize the general form of a polar equation of a circle centered at (0,0) which is r=Rcos⁡(θ) or r=Rsin⁡(θ), where R is the radius of the circle.

Step 2 ：Step 2: By comparing the given equation r=3cos⁡(θ) with the general form, we can see that R=3. Therefore, the radius of the circle is 3.

Step 3 ：Step 3: The center of the circle in polar coordinates is always (0,0) for equations of the form r=Rcos⁡(θ) or r=Rsin⁡(θ). So, the center of this circle is (0,0).

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