Hello!
The directrix of a parabola is a fixed line used in describing a curve or surface.
The standard form a parabola is 4p(x - h) = (y - k)². In this equation, h, k is the vertex, and p is the focal point.
To find the standard form, first, we would find p.
Since the equation given, y² = -24x, has a vertex at (0, 0), h, k would be zero. In this case, we can find p now.
4p = -24 (divide both sides by 4)
p = -6
4(-6)(x - 0) = (y - 0)² which can be simplified to: 4(-6)(x) = y².
Looking at the graph of the parabola, it is symmetric around the x-axis, so therefore, the directrix is a line parallel to the y-axis. To find the directrix, use the formula: x = 0 - p, and we know that p = -6.
x = 0 - (-6)
x = 6
Therefore, the directrix of the parabola is choice D, x = 6.
