JEE Advanced 2021 Paper 1

Let α,β and γ be real numbers such that the system of linear equations
x+2y+3z=α
4x+5y+6z=β
7x+8y+9z=γ−1
is consistent. Let |M| represent the determinant of the matrix
M=[

α	2	γ
β	1	0
−1	0	1

]
Let P be the plane containing all those (α,β,γ) 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.