Answer
$\{ 9\pm\sqrt {119}\}$
Work Step by Step
Step 1. Use the distance formula: $\sqrt {(3-(-2))^2+(y-9)^2}=12$
Step 2. Take square on both sides: $25+y^2-18y+81=144$ or $y^2-18y-38=0$
Step 3. Solve the equation to get $y=\frac{18\pm\sqrt {18^2+4(38)}}{2}=9\pm\sqrt {119}$
Step 4. The solution set is $\{ 9\pm\sqrt {119}\}$
