Đáp án: $m = 4;B\left( { - 2;8} \right)$
Giải thích các bước giải:
$\begin{array}{l}
A\left( {1;2} \right) \in \left( d \right)\\
\Leftrightarrow 2 = - 2.1 + {m^2} - 12\\
\Leftrightarrow 2 = {m^2} - 14\\
\Leftrightarrow {m^2} = 16\\
\Leftrightarrow \left[ \begin{array}{l}
m = 4\\
m = - 4
\end{array} \right.\left( 1 \right)\\
A\left( {1;2} \right) \in \left( P \right)\\
\Leftrightarrow 2 = \left( {m - 2} \right){.1^2}\\
\Leftrightarrow m - 2 = 2\\
\Leftrightarrow m = 4\left( 2 \right)\\
\left( 1 \right);\left( 2 \right) \Leftrightarrow m = 4\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( d \right):y = - 2x + 4\\
\left( P \right):y = 2{x^2}
\end{array} \right.\\
Xet:2{x^2} = - 2x + 4\\
\Leftrightarrow {x^2} + x - 2 = 0\\
\Leftrightarrow \left( {x - 1} \right)\left( {x + 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1;y = 2{x^2} = 2\\
x = - 2;y = 2{x^2} = 8
\end{array} \right.\\
Vậy\,B\left( { - 2;8} \right)
\end{array}$
