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Section 3.3 : Circles

1. Write the equation of the circle with radius 3 and center \(\left( {6,0} \right)\). Solution
2. Write the equation of the circle with radius \(\sqrt 7 \) and center \(\left( { - 1, - 9} \right)\). Solution

For problems 3 – 5 determine the radius and center of the circle and sketch the graph of the circle.

1. \({\left( {x - 9} \right)^2} + {\left( {y + 4} \right)^2} = 25\) Solution
2. \({x^2} + {\left( {y - 5} \right)^2} = 4\) Solution
3. \({\left( {x + 1} \right)^2} + {\left( {y + 3} \right)^2} = 6\) Solution

For problems 6 – 8 determine the radius and center of the circle. If the equation is not the equation of a circle clearly explain why not.

1. \({x^2} + {y^2} + 14x - 8y + 56 = 0\) Solution
2. \(9{x^2} + 9{y^2} - 6x - 36y - 107 = 0\) Solution
3. \({x^2} + {y^2} + 8x + 20 = 0\) Solution