Đáp án: m=17
Giải thích các bước giải:
$\begin{array}{l}
b)y = mx - m + 1\\
Cho:x = 0 \Rightarrow y = - m + 1\\
\Rightarrow H\left( {0; - m + 1} \right)\\
Xet:{x^2} = mx - m + 1\\
\Rightarrow {x^2} - mx + m - 1 = 0\\
\Rightarrow \left( {x - 1} \right)\left( {x - m + 1} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 1\\
x = m - 1
\end{array} \right.\\
\Rightarrow {x_B} = \left( {m - 1} \right)\\
\Rightarrow {y_B} = {\left( {m - 1} \right)^2}\\
\Rightarrow B\left( {m - 1;{{\left( {m - 1} \right)}^2}} \right)\\
\Rightarrow BH = \sqrt {{{\left( {m - 1} \right)}^2} + {{\left( {{m^2} - 2m + 1 + m - 1} \right)}^2}} \\
= \sqrt {{{\left( {m - 1} \right)}^2} + {{\left( {{m^2} - m} \right)}^2}} \\
= \sqrt {{{\left( {m - 1} \right)}^2}.\left( {{m^2} + 1} \right)} \left( {dk:m > 1} \right)\\
= \left( {m - 1} \right)\sqrt {{m^2} + 1} \\
{d_{O - BH}} = {d_{O - d}}\\
\left( d \right):y = mx - m + 1\\
\Rightarrow mx - y - m + 1 = 0\\
\Rightarrow {d_{O - d}} = \dfrac{{\left| {m.0 - 0 - m + 1} \right|}}{{\sqrt {{m^2} + 1} }} = \dfrac{1}{{\sqrt {{m^2} + 1} }}\\
\Rightarrow {S_{OBH}} = \dfrac{1}{2}.{d_{O - BH}}.BH = 8\\
\Rightarrow \dfrac{1}{2}.\dfrac{1}{{\sqrt {{m^2} + 1} }}.\left( {m - 1} \right)\sqrt {{m^2} + 1} = 8\\
\Rightarrow m - 1 = 16\\
\Rightarrow m = 17\left( {tmdk} \right)
\end{array}$
Vậy m=17
