a.
Ta có: \(\left\{{}\begin{matrix}-4a=-2\\8b=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=2\\b=-4\end{matrix}\right.\) \(\Rightarrow I\left(2;-4\right)\)
\(R=\sqrt{2^2+\left(-4\right)^2+5}=5\)
b.
PTTT: \(\left(C\right):\left(a-x_0\right)\left(x-x_0\right)+\left(b-y_0\right)\left(y-y_0\right)=0\)
\(\Leftrightarrow\left(2+1\right)\left(x+1\right)+\left(-4-0\right)\left(y-0\right)=0\)
\(\Leftrightarrow\left(C\right):3x-4y=-3\)
c.
Ta có: \(\Delta\perp d\Rightarrow\Delta:4x+3y+c=0\)
\(d\left(I,\Delta\right):\dfrac{\left|4\cdot2-3\cdot4+c\right|}{\sqrt{4^2+3^2}}=5\)
\(\Leftrightarrow\left|c-4\right|=25\) \(\Leftrightarrow\left[{}\begin{matrix}c=29\\c=-21\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\Delta:4x+3y+29=0\\\Delta:4x+3y-21=0\end{matrix}\right.\)