Step 1:

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The equation is $\"\"$ .

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The polar coordinates are related to Cartesian coordinates by the equation $\"\"$ .

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Where $\"\"$ .

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Change the polar equation into Cartesian equation.

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$\"\"$

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Multiply each side by $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ . $\"\"$

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Change the expressions $\"\"$ into a perfect square trinomial,

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add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation.

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$\"\"$

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$\"\"$

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Compare above equation with circle standard equation $\"\"$ .

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Where $\"\"$ is center of circle and $\"\"$ is the radius of circle.

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The equation $\"\"$ is in the form of circle equation $\"\"$ .

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center of circle is $\"\"$ .

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Radius of circle is $\"\"$ .

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Solution:

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The circle equation is $\"\"$ .

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center of circle is $\"\"$ .

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Radius of circle is $\"\"$ .

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