Giúp mik vs, mik đội ơn

Gọi $(P)$ là mặt phẳng cần tìm có phương trình là $ax+by+cz+d=0$ với điều kiện $a^2+b^2+c^2\ne 0$

Vì mặt phẳng$(P)$ đi qua $M$ nên:

$\begin{array}{l}
a.0 - 2b + c.0 + d = 0 \Leftrightarrow d = 2b\\
 \Rightarrow \left( P \right):ax + by + cz + 2b = 0
\end{array}$

Lại có: 

$\left\{ \begin{array}{l} \left( P \right)//\Delta \\ {d_{\left( {\Delta ,\left( P \right)} \right)}} = 4 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} \overrightarrow {{n_P}} .\overrightarrow {{u_\Delta }}  = 0\\ {d_{\left( {A ,\left( P \right)} \right)}} = 4 \end{array} \right.$

với $A(1;3;0)$
$\begin{array}{l}
\left\{ \begin{array}{l}
\overrightarrow {{n_P}} .\overrightarrow {{u_\Delta }}  = 0\\
{d_{\left( {\Delta ,\left( P \right)} \right)}} = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a.1 + b.1 + 4c = 0\\
\dfrac{{\left| {a.1 + b.3 + c.0 + 2b} \right|}}{{\sqrt {{a^2} + {b^2} + {c^2}} }} = 4
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
a + b + 4c = 0\\
\dfrac{{\left| {a + 5b} \right|}}{{\sqrt {{a^2} + {b^2} + {c^2}} }} = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
{\left( {a + 5b} \right)^2} = 16\left( {{a^2} + {b^2} + {c^2}} \right)\\
a + b + 4c = 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
{a^2} + 10ab + 25{b^2} = 16{a^2} + 16{b^2} + 16{c^2}\\
a + b + 4c = 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
15{a^2} - 9{b^2} + 16{c^2} - 10ab = 0\\
a + b + 4c = 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
15{a^2} - 9{b^2} + {\left( { - a - b} \right)^2} - 10ab = 0\\
a + b + 4c = 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
16{a^2} - 8{b^2} - 8ab = 0\\
a + b + 4c = 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
a = b\\
a =  - \dfrac{1}{2}b
\end{array} \right.\\
a + b + 4c = 0
\end{array} \right.\\
a = b \to a = 2 \to b = 2 \to c =  - 1\\
 \Rightarrow \left( P \right):2x + 2y - z + 4 = 0\\
a =  - \dfrac{1}{2}b \to a = 4 \to b =  - 8 \to c = 1\\
 \Rightarrow \left( P \right):4x - 8y + z - 16 = 0\\
 \to C
\end{array}$