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Section 3-3 : Circles

1. Write the equation of the circle with radius 1 and center $$\left( {11,4} \right)$$.
2. Write the equation of the circle with radius 10 and center $$\left( { - 6,0} \right)$$.
3. Write the equation of the circle with radius $$\sqrt {19}$$ and center $$\left( {7, - 2} \right)$$.
4. Write the equation of the circle with radius $$\frac{7}{3}$$ and center $$\displaystyle \left( { - \frac{1}{2},\frac{3}{4}} \right)$$.

For problems 5 – 10 determine the radius and center of the circle and sketch the graph of the circle.

1. $${\left( {x + 8} \right)^2} + {y^2} = 36$$
2. $${\left( {x - 1} \right)^2} + {\left( {y - 7} \right)^2} = 16$$
3. $${\left( {x + 10} \right)^2} + {\left( {y - 6} \right)^2} = 25$$
4. $$\displaystyle {x^2} + {\left( {y + 4} \right)^2} = \frac{{49}}{{144}}$$
5. $${\left( {x + 2} \right)^2} + {\left( {y - 1} \right)^2} = 3$$
6. $${\left( {x - 5} \right)^2} + {\left( {y - 3} \right)^2} = 11$$

For problems 11 – 17 determine the radius and center of the circle. If the equation is not the equation of a circle clearly explain why not.

1. $${x^2} + {y^2} - 8y = 0$$
2. $${x^2} + {y^2} - 6x - 4y - 12 = 0$$
3. $${x^2} + {y^2} + 12x + 2y + 28 = 0$$
4. $$16{x^2} + 16{y^2} - 16x + 8y - 11 = 0$$
5. $$2{x^2} + 2{y^2} - 3x + 1 = 0$$
6. $${x^2} + {y^2} + 2x - 2y + 11 = 0$$
7. $${x^2} + {y^2} - 10x + 4y + 29 = 0$$