Answer
(a) center $(-4, 0)$, vertices $V_1(-8,0)$ and $V_2(0,0)$, foci $F(\pm4\sqrt 2-4, 0)$. asymptotes $y=\pm (x+4)$
(b) See graph.
Work Step by Step
(a) Step 1. Write the given equation as $\frac{(x+4)^2}{16}-\frac{y^2}{16}=1$
Step 2. Identify the center as $(-4, 0)$
Step 3. Identify $a=4, b=4, c=\sqrt {16+16}=4\sqrt 2$
Step 4. The original vertices are $(\pm4, 0)$, vertices after the shift $V_1(-8,0)$ and $V_2(0,0)$
Step 5. Original foci $(\pm 4\sqrt 2, 0)$, foci after shift $F(\pm4\sqrt 2-4, 0)$.
Step 6. Original asymptotes $y=\pm x$, new asymptotes $y=\pm (x+4)$
(b) See graph.
