The shape ``$\varnothing$'' can be made into a beautiful ribbon. Consider it as part of the curve $C$ in the figure. It is known that $C$ passes through the origin $O$ , and points on $C$ satisfy: the abscissa is greater than $- 2$ , and the product of the distance to point $F ( 2,0 )$ and the distance to the line $x = a ( a < 0 )$ equals 4 . Then A. $a = - 2$ B. The point $( 2 \sqrt { 2 } , 0 )$ is on $C$ C. The maximum ordinate of points on $C$ in the first quadrant is 1 D. When point $\left( x _ { 0 } , y _ { 0 } \right)$ is on $C$ , $y _ { 0 } \leqslant \frac { 4 } { x _ { 0 } + 2 }$
The shape ``$\varnothing$'' can be made into a beautiful ribbon. Consider it as part of the curve $C$ in the figure. It is known that $C$ passes through the origin $O$ , and points on $C$ satisfy: the abscissa is greater than $- 2$ , and the product of the distance to point $F ( 2,0 )$ and the distance to the line $x = a ( a < 0 )$ equals 4 . Then\\
A. $a = - 2$\\
B. The point $( 2 \sqrt { 2 } , 0 )$ is on $C$\\
C. The maximum ordinate of points on $C$ in the first quadrant is 1\\
D. When point $\left( x _ { 0 } , y _ { 0 } \right)$ is on $C$ , $y _ { 0 } \leqslant \frac { 4 } { x _ { 0 } + 2 }$