Write the equation for a parabola with the focus at (–1, 4) and the equation of the directrix x = 5.

The directrix is the vertical line x = 5, so the parabola opens horizontally and its axis is y = 4. The vertex lies halfway between the focus at x = −1 and the directrix at x = 5, giving vertex (2, 4); the focus is 3 units left of it, so p = −3. Using (y − k)² = 4p(x − h), the equation is (y − 4)² = −12(x − 2), choice D.

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