Section 3.3 : Circles
- Write the equation of the circle with radius 1 and center \(\left( {11,4} \right)\).
- Write the equation of the circle with radius 10 and center \(\left( { - 6,0} \right)\).
- Write the equation of the circle with radius \(\sqrt {19} \) and center \(\left( {7, - 2} \right)\).
- 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.
- \({\left( {x + 8} \right)^2} + {y^2} = 36\)
- \({\left( {x - 1} \right)^2} + {\left( {y - 7} \right)^2} = 16\)
- \({\left( {x + 10} \right)^2} + {\left( {y - 6} \right)^2} = 25\)
- \(\displaystyle {x^2} + {\left( {y + 4} \right)^2} = \frac{{49}}{{144}}\)
- \({\left( {x + 2} \right)^2} + {\left( {y - 1} \right)^2} = 3\)
- \({\left( {x - 5} \right)^2} + {\left( {y - 3} \right)^2} = 11\)
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.
- \({x^2} + {y^2} - 8y = 0\)
- \({x^2} + {y^2} - 6x - 4y - 12 = 0\)
- \({x^2} + {y^2} + 12x + 2y + 28 = 0\)
- \(16{x^2} + 16{y^2} - 16x + 8y - 11 = 0\)
- \(2{x^2} + 2{y^2} - 3x + 1 = 0\)
- \({x^2} + {y^2} + 2x - 2y + 11 = 0\)
- \({x^2} + {y^2} - 10x + 4y + 29 = 0\)