Answer
$\frac{(x-4)^2}{4}-\frac{(y+1)^2}{5}=1$.
See graph.
Work Step by Step
1. Given center $(4,-1)$, focus $(7,-1)$, vertex $(6,-1)$, we can identify the transverse axis as $x$-axis, $a=6-4=2, c=7-4=3$ and $b^2=c^2-a^2=9-4=5$. Thus we have the equation $\frac{(x-4)^2}{4}-\frac{(y+1)^2}{5}=1$.
2. See graph.
