Let the coordinate be as follows.
[tex](x,y)=\mleft(-\frac{8}{9},a\mright)[/tex]
Substitute the coordinates into the equation.
[tex]\mleft(-\frac{8}{9}\mright)^2+a^2=1[/tex]
Simplify the left side of the equation.
[tex]\frac{64}{81}+a^2=1[/tex]
Subtract both sides of the equation by 64/81.
[tex]\begin{gathered} a^2=1-\frac{64}{81} \\ =\frac{81}{81}-\frac{64}{81} \\ =\frac{17}{81} \end{gathered}[/tex]
To obtain the value of a, use the square root property. Find the square root of both sides of the equation.
[tex]a=\pm\sqrt[]{\frac{17}{81}}=\pm\frac{\sqrt[]{17}}{9}[/tex]
Thus, the values of a is as follows.
[tex]a=\frac{\sqrt[]{17}}{9}\text{and -}\frac{\sqrt[]{17}}{9}[/tex]
