Question

A normal with slope $\frac{1}{\sqrt6}$ is drawn from the point (0, -α) to the parabola x2 = -4αy, where a > 0. Let L be the line passing through (0, -α) and parallel to the directrix of the parabola. Suppose that L intersects the parabola at two points A and B. Let r denote the length of the latus rectum and s denote the square of the length of the line segment AB. If r : s = 1 : 16 then the value of 24a is __________.

Answer 1

The correct answer is: 12.