Question

$${ x }^{ 2 } + { y }^{ 2 } -6x-6y=7$$

Answer

x=3+IM*sqrt((y-8)*(y+2)),3-IM*sqrt((y-8)*(y+2))

Solution


Move all terms to one side.
\[{x}^{2}+{y}^{2}-6x-6y-7=0\]
Use the Quadratic Formula.
\[x=\frac{6+2\imath \sqrt{(y-8)(y+2)}}{2},\frac{6-2\imath \sqrt{(y-8)(y+2)}}{2}\]
Simplify solutions.
\[x=3+\imath \sqrt{(y-8)(y+2)},3-\imath \sqrt{(y-8)(y+2)}\]