\left\{ \begin{array} { l } { x ^ { 2 } - 2 x + | y | - 15 = 0 } \\ { x ^ { 2 } + ( y - a ) ( y + a ) = 2 ( x - \frac { 1 } { 2 } ) } \end{array} \right.
Solve for x, y
\left\{\begin{matrix}x=-\sqrt{-|\frac{-\sqrt{4a^{2}-63}+1}{2}|+16}+1\text{, }y=\frac{-\sqrt{4a^{2}-63}+1}{2}\text{; }x=-\sqrt{-|\frac{\sqrt{4a^{2}-63}-1}{2}|+16}+1\text{, }y=\frac{\sqrt{4a^{2}-63}-1}{2}\text{; }x=\sqrt{-|\frac{-\sqrt{4a^{2}-63}+1}{2}|+16}+1\text{, }y=\frac{-\sqrt{4a^{2}-63}+1}{2}\text{; }x=\sqrt{-|\frac{\sqrt{4a^{2}-63}-1}{2}|+16}+1\text{, }y=\frac{\sqrt{4a^{2}-63}-1}{2}\text{, }&\left(a\geq -4\text{ and }a\leq -\frac{3\sqrt{7}}{2}\right)\text{ or }\left(a\geq \frac{3\sqrt{7}}{2}\text{ and }a\leq 4\right)\\x=-\frac{\sqrt{-2\sqrt{4a^{2}-63}+62}}{2}+1\text{, }y=\frac{\sqrt{4a^{2}-63}+1}{2}\text{; }x=-\frac{\sqrt{-2\sqrt{4a^{2}-63}+62}}{2}+1\text{, }y=\frac{-\sqrt{4a^{2}-63}-1}{2}\text{; }x=\frac{\sqrt{-2\sqrt{4a^{2}-63}+62}}{2}+1\text{, }y=\frac{\sqrt{4a^{2}-63}+1}{2}\text{; }x=\frac{\sqrt{-2\sqrt{4a^{2}-63}+62}}{2}+1\text{, }y=\frac{-\sqrt{4a^{2}-63}-1}{2}\text{, }&\left(a\geq -16\text{ and }a\leq -\frac{3\sqrt{7}}{2}\right)\text{ or }\left(a\geq \frac{3\sqrt{7}}{2}\text{ and }a\leq 16\right)\end{matrix}\right.
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