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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

Let & LL^ ' be the latus rectum through the focus S of a hyperbola...

Let & LL′LL^{'} be the latus rectum through the focus SS of a hyperbola and AA~be the farther vertex of the conic. If ΔALL′\Delta ALL^{'} is equilateral then its eccentricity isLet & LL^ ' be the latus rectum through the focus S of a hyperbola and A ~be the farther vertex of the conic. If Δ ALL^

Options

  1. A3\sqrt{3}
  2. B3+1\sqrt{3} + 1
  3. C\left(\sqrt{3} + 1\right)\sqrt{2}
  4. D1+131 + \dfrac{1}{\sqrt{3}}

Correct answer

D. 1+131 + \dfrac{1}{\sqrt{3}}

Step-by-step solution

& & & & & & & Let & LL^ ' be the latus rectum through the focus S of a hyperbola and A ~be the farther vertex of the conic. If Δ ALL^

AM=a+aeAM = a + ae

ML′=b2aML^{'} = \dfrac{b2}{a}

θ=30°\theta = 30 °

⇒(b2a)a+ae=13⇒ \left(\dfrac{b2}{a}\right)a + ae = \dfrac{1}{3}

⇒b2a2=e+13⇒ \dfrac{b2}{a2} = \dfrac{e + 1}{3}

⇒e2−1=e+13⇒ e^{2} - 1 = \dfrac{e + 1}{3}

⇒e−1=13⇒ e - 1 = \dfrac{1}{3}

⇒e=1+13⇒ e = 1 + \dfrac{1}{3}

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