Appendix A - Appendix A Exercises - Page 1158: 35

$$y = 2 - \sqrt {9 - {{\left( {x + 1} \right)}^2}} $$

$$\eqalign{ & {\text{Let the center be }}\left( { - 1,2} \right){\text{ and then radius be }}r = 3. \cr & {\text{The standard form equation of a circle centered at }}\left( {h,k} \right){\text{ and}} \cr & {\text{radius }}r\,{\text{is :}} \cr & {\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2} \cr & {\text{Substituting }}\underbrace {\left( { - 1,2} \right)}_{\left( {h,k} \right)}{\text{ and }}r = 3 \cr & {\left[ {x - \left( { - 1} \right)} \right]^2} + {\left( {y - 2} \right)^2} = {\left( 3 \right)^2} \cr & {\left( {x + 1} \right)^2} + {\left( {y - 2} \right)^2} = 9 \cr & {\text{Solving the equation for }}y \cr & {\left( {y - 2} \right)^2} = 9 - {\left( {x + 1} \right)^2} \cr & y - 2 = \pm \sqrt {9 - {{\left( {x + 1} \right)}^2}} \cr & y = 2 \pm \sqrt {9 - {{\left( {x + 1} \right)}^2}} \cr & {\text{Where:}} \cr & \left( {{\text{equation of the upper half of the circle}}} \right) \cr & y = 2 + \sqrt {9 - {{\left( {x + 1} \right)}^2}} , \cr & \left( {{\text{equation of the lower half of the circle}}} \right) \cr & y = 2 - \sqrt {9 - {{\left( {x + 1} \right)}^2}} \cr} $$