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.