Answer
parabola, vertex $V(-64, 8)$, focus $F(-\frac{255}{4}, 8)$, directrix $x=-\frac{257}{4}$
See graph.
Work Step by Step
Step 1. Identify the type of the conics: rewrite the equation as $y^2-16y+64=x+64$ or $(y-8)^2=(x+64)$, and the equation is of the form of a parabola (opening to the right).
Step 2. The vertex can be found at $V(-64, 8)$
Step 3. With $4p=1$, we get $p=\frac{1}{4}$, so the focus is at $(p-64, 8)$ or $F(-\frac{255}{4}, 8)$
Step 4. The directrix can be found as $x=-p-64=-\frac{257}{4}$
Step 5. See graph.
