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Hyperbola question

2024 · 6 Apr · Shift 2 · Q55

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Hyperbola
2024 · 6 Apr · Shift 2 · Q55

Hyperbola question

2024 · 6 Apr · Shift 2 · Q55

JEE MainMathematicsHyperbolaNumerical+4 / −1

The length of the latus rectum and directrices of hyperbola with eccentricity e are 9 and

x= \pm \frac{4}{\sqrt{3}}

, respectively. Let the line

y-\sqrt{3} x+\sqrt{3}=0

touch this hyperbola at

\left(x_0, y_0\right)

. If

\mathrm{m}

is the product of the focal distances of the point

\left(x_0, y_0\right)

, then

4 \mathrm{e}^2+\mathrm{m}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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