Gọi `(Q): Ax+By+Cz+D=0`

`=>` `vec(n_(Q))=(A; B; C)`

Xét: `vec(n_(Q))*vec(i)=0<=>A=0`

Mà `O(0;0;0) in (Q)=>D=0`

`=>` `(Q): By+Cz=0`

Giả sử `B ne 0=>(Q): y+C/Bz=0`

Đặt `C/B=k=>(Q): y+kz=0`

Xét: `d(I,(Q))=(|-2+k|)/(sqrt(0^2+1^2+k^2))=sqrt5`

`<=>` `|k-2|=sqrt5*sqrt(1+k^2)`

`<=>` `k^2-4k+4=5k^2+5`

`<=>` `4k^2+4k+1=0`

`<=>` `k=-1/2``

`=>` `(Q): y-1/2z=0<=>2y-z=0`

`=>` $\fbox{Đúng}$