Step-by-Step Solution
Key Concept: For parabola y² = 4ax, the directrix is x = -a. A normal at parameter t has equation y = -t·y + 2at + at³, and from an external point, the number of normals depends on whether the point lies on the directrix (exactly 1 normal) or other positions. The relationship between normal count and point location on directrix vs other curves requires analyzing the normal equation y + tx = 2at + at³.
Points $(-1, 2)$ and $(-1, -5)$ lie on the directrix of parabola $y^2 = 4x$. From a point on the directrix, only one normal to the parabola can be drawn, since the directrix is perpendicular to the axis and the parabola is symmetric about its axis. This means at most one normal passes through any single point on the directrix.
Correct Answer: [A-p, r] [B-p, q, r] [C-q] [D-q, s]