JEE Advanced 2021 Paper 1

Paragraph for next 2 questions Let $\alpha, \beta$ and $\gamma$ be real numbers such that the system of linear equations $x+2y+3z=\alpha$ $4x+5y+6z=\beta$ $7x+8y+9z=\gamma-1$ is consistent. Let $\left| M \right|$ represent the determinant of the matrix $M=\begin{bmatrix} \alpha & 2 & \gamma \\ \beta & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix}$ Let $P$ be the plane containing all those $(\alpha, \beta, \gamma)$ for which the above system of linear equations is consistent, and D be the square of the distance of the point $(0,1,0)$ from the plane $P$.