\left. \begin{array} { l } { ext { A Circle in Polar Coordinates Consider the polar equation } } \ { r = a \cos heta + b \sin heta ext { . } } \ { ext { (a) Express the equation in rectangular coordinates, and use } } \ { ext { this to show that the graph of the equation is a circle. } } \ { ext { What are the center and radius? } } \ { ext { (b) Use your answer to part (a) to graph the equation } } \ { r = 2 \sin heta + 2 \cos heta ext { . } } \end{array} ight.

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\left. \begin{array} { l } { 	ext { A Circle in Polar Coordinates Consider the polar equation } } \ { r = a \cos 	heta + b \sin 	heta 	ext { . } } \ { 	ext { (a) Express the equation in rectangular coordinates, and use } } \ { 	ext { this to show that the graph of the equation is a circle. } } \ { 	ext { What are the center and radius? } } \ { 	ext { (b) Use your answer to part (a) to graph the equation } } \ { r = 2 \sin 	heta + 2 \cos 	heta 	ext { . } } \end{array} ight.

Riley Mcdonald · Accepted Answer

$$\left. \begin{array} { l } { 	ext { (a) } ( x - \frac { a } { 2 } ) ^ { 2 } + ( y - \frac { b } { 2 } ) ^ { 2 } = \frac { a ^ { 2 } + b ^ { 2 } } { 4 } } \ { ( \frac { a } { 2 } , \frac { b } { 2 } ) , \frac { 1 } { 2 } \sqrt { a ^ { 2 } + b ^ { 2 } } } \ { 	ext { (b) } } \end{array} ight.$$

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