Consider points $P ( x , y )$ on the coordinate plane satisfying the equation $\frac { 2 ^ { x ^ { 2 } } } { 8 } = \frac { 4 ^ { x } } { 2 ^ { y ^ { 2 } } }$. Select the correct options. (1) When $x = 3$, there are 2 distinct solutions satisfying this equation (2) If point $( a , b )$ satisfies this equation, then point $( - a , - b )$ also satisfies this equation (3) All possible points $P ( x , y )$ form a circle (4) Point $P ( x , y )$ may lie on the line $x + y = 4$ (5) For all possible points $P ( x , y )$, the maximum value of $x - y$ is $1 + 2 \sqrt { 2 }$
Consider points $P ( x , y )$ on the coordinate plane satisfying the equation $\frac { 2 ^ { x ^ { 2 } } } { 8 } = \frac { 4 ^ { x } } { 2 ^ { y ^ { 2 } } }$. Select the correct options.\\
(1) When $x = 3$, there are 2 distinct solutions satisfying this equation\\
(2) If point $( a , b )$ satisfies this equation, then point $( - a , - b )$ also satisfies this equation\\
(3) All possible points $P ( x , y )$ form a circle\\
(4) Point $P ( x , y )$ may lie on the line $x + y = 4$\\
(5) For all possible points $P ( x , y )$, the maximum value of $x - y$ is $1 + 2 \sqrt { 2 }$