1. **State the problem:** Find the equation of the parabola with focus at $(-17, 1)$ and directrix $x = 1$. 2. **Recall the definition and formula:** A parabola is the set of points equidistant from the focus and the directrix. 3. Since the directrix is vertical ($x=1$), the parabola opens horizontally. 4. The vertex lies midway between the focus and directrix on the horizontal axis. 5. Calculate the vertex $V$: $$V_x = \frac{-17 + 1}{2} = \frac{-16}{2} = -8$$ $$V_y = 1$$ So, vertex $V = (-8, 1)$. 6. The distance $p$ from vertex to focus (or vertex to directrix) is: $$p = |V_x - (-17)| = |-8 + 17| = 9$$ 7. Since the parabola opens left (focus is left of vertex), $p = -9$. 8. The standard form of a horizontal parabola with vertex $(h,k)$ is: $$ (y - k)^2 = 4p(x - h) $$ 9. Substitute $h = -8$, $k = 1$, and $p = -9$: $$ (y - 1)^2 = 4(-9)(x + 8) $$ $$ (y - 1)^2 = -36(x + 8) $$ **Final answer:** $$\boxed{(y - 1)^2 = -36(x + 8)}$$