Ans: A
The coordinates of the centre of the circle
The coordinates of the centre of the circle
$\begin{array}{cl}
= & \left( – \dfrac{-8}{2}, – \dfrac{k}{2} \right) \\
= & (4, \dfrac{-k}{2})
\end{array}$
Note that the diameter passes through the centre and the point $(6,-5)$, and its slope is $-4$. Hence, we have
$\begin{array}{rcl}
\dfrac{\frac{-k}{2} – (-5)}{4-6} & = & -4 \\
\dfrac{-k}{2} + 5 & = & 8 \\
\dfrac{-k}{2} & = & 3 \\
k & = & -6
\end{array}$
