Strange Perpendicular Chords

Geometry Level 4

Two mutually perpendicular chords are drawn from the vertex of parabola such that their lengths are \(8\) and \(27\). This is possible for only one distance between the parabola's focus and the directrix.

The length of latus rectum of such a parabola can be expressed as \( \displaystyle \frac{a}{\sqrt{b}} \) where \( a\) and \(b\) are positive coprime integers and \(b\) is square-free .

Enter the value of \( a+b\).

Details and Assumptions:

  • Latus rectum is the focal chord of a parabola which is perpendicular to the axis of the parabola.

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