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Parabola question

2024 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Parabola
2024 · Shift 2 · Q29

Parabola question

2024 · Shift 2 · Q29

JEE AdvancedMathematicsParabolaNumerical+4 / −1

A normal with slope

\frac{1}{\sqrt{6}}

is drawn from the point

(0,-\alpha)

to the parabola

x^2=-4 a y

, where

a\gt 0

. Let

L

be the line passing through

(0,-\alpha)

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

A B

. If

r: s=1: 16

, then the value of

24 a

is

\underline{\hspace{2cm}}

.

Numerical answer

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