Ans: A
Note that the centre of the circle
Note that the centre of the circle
$\begin{array}{cl}
= & \left( \dfrac{-(-4)}{2}, \dfrac{-(6)}{2} \right) \\
= & (2,-3)
\end{array}$
Therefore, the slope of the diameter passing through the point $(1,2)$
$\begin{array}{cl}
= & \dfrac{-3-2}{2-1} \\
= & -5
\end{array}$
