The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and {\x}= \pm {4}/{\sqrt{3}}, respectively. Let the line y-\sqrt{3} {\x}+\sqrt{3}=0 touch this hyperbola at ( {\x}_0, {\y}_0). If {\m} is the product of the focal distances of the point ( {\x}_0, {\y}_0), then 4 {\e}^2+ {\m} is equal to _______. [6 Apr 2024 Shift 2]

Hyperbola

Section: Mathematics

Question : 20 of 92

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The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and x=±‌

√3

, respectively. Let the line y−√3x+√3=0 touch this hyperbola at (x0,y0). If m is the product of the focal distances of the point (x0,y0), then 4e2+m is equal to _______.

[6 Apr 2024 Shift 2]

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