There are several issues to consider.
1, because it is parallel to the y axis, the coefficient before y must be 0, and a = 1 or a = 2/3 can be obtained.
2. when a = what and x = 0, a = 2/3 or x =- 1/2 is obtained.
It is found that when a = 2/3, the coefficients in front of X and Y are both 0.
Continue with step three. 3. When A = 2/3, the equal sign does not hold.
The original equal sign does not hold (if it holds, it means that the equations of X and Y hold no matter what value they take when a = 2/3, that is, the equation represents an xoy plane, but the Y axis belongs to this plane, even if the equation holds).
3. When A = 1, X = 0 is the Y axis, and the coincidence parallelism is different, so it should be discarded.
So option d does not exist.