\left\{ \begin{array} { l } { A C B D = \frac { 4 } { 9 } } \\ { ( \frac { A C } { 2 } ) ^ { 2 } + ( \frac { B D } { 2 } ) ^ { 2 } = 1 } \end{array} \right.
Solve for A, C, B, D
A=\frac{4}{9BCD}\text{, }C\neq 0\text{, }B=\frac{\sqrt{7}+\sqrt{11}}{3|D|}\text{, }D\neq 0
A=\frac{4}{9BCD}\text{, }C\neq 0\text{, }B=-\frac{\sqrt{7}+\sqrt{11}}{3|D|}\text{, }D\neq 0
A=\frac{4}{9BCD}\text{, }C\neq 0\text{, }B=\frac{\sqrt{11}-\sqrt{7}}{3|D|}\text{, }D\neq 0
A=\frac{4}{9BCD}\text{, }C\neq 0\text{, }B=-\frac{\sqrt{11}-\sqrt{7}}{3|D|}\text{, }D\neq 0\text{, }D\neq 0
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