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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 __________.
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 __________.
Updated On: Jul 21, 2024
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Correct Answer: 12
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The correct answer is: 12.
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