Step 1: Shift the origin
Move to $X = x - 1$, $Y = y + 2$. The equation becomes $7X^2 + 16Y^2 = 448$.
Step 2: Semi-axes
$a^2 = \frac{448}{7} = 64$ and $b^2 = \frac{448}{16} = 28$. Since $a^2 > b^2$, $a = 8$ is the semi-major axis.
Step 3: Focal distance
$c^2 = a^2 - b^2 = 36$, so $c = 6$ and $e = \frac{c}{a} = \frac{6}{8}$.
Step 4: Result
$e = \frac{3}{4}$. The value $\frac{\sqrt{7}}{4}$ equals $b/a$ for this ellipse, not $e$.
Final Answer:
The eccentricity is 3/4. This is option (A).
\[ \boxed{\text{(A) }\frac{3}{4}} \]