JEE Advanced 2015 · Paper 1, Mathematics question 51

In $\mathbb R^3$, consider the planes $P_1:y=0$ and $P_2:x+z=1$. Let $P_3$ be a plane, different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2$. If the distance of the point $(0,1,0)$ from $P_3$ is 1 and the distance of a point $(\alpha,\beta,\gamma)$ from $P_3$ is 2, then which of the following relations is (are) true?