Question

Let $H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, where $a>b>0$, be a hyperbola in the $xy$-plane whose conjugate axis $LM$ subtends an angle of $60^{0}$ at one of its vertices $N$. Let the area of the triangle $LMN$ be $4 \sqrt{3}$.

| LIST-I | | LIST-II | |
| --- | --- | --- | --- |
| P. | The length of the conjugate axis of $H$ is | 1. | 8 |
| Q. | The eccentricity of $H$ is | 2. | $\frac{4}{\sqrt{3}}$ |
| R. | The distance between the foci of $H$ is | 3. | $\frac{2}{\sqrt{3}}$ |
| S. | The length of the latus rectum of $H$ is | 4. | 4 |

The correct option is:

Accepted Answer

(B) $\mathbf{P} \rightarrow \mathbf{4 ;} \mathbf{Q} \rightarrow \mathbf{3 ;} \mathbf{R} \rightarrow \mathbf{1} ; \mathbf{S} \rightarrow \mathbf{2}$

Answer

(A) $\mathbf{P} \rightarrow \mathbf{4} ; \mathbf{Q} \rightarrow \mathbf{2} ; \mathbf{R} \rightarrow \mathbf{1} ; \mathbf{S} \rightarrow \mathbf{3}$

Answer

(C) $\mathbf{P} \rightarrow \mathbf{4 ;} \mathbf{Q} \rightarrow \mathbf{1} ; \mathbf{R} \rightarrow \mathbf{3} ; \mathbf{S} \rightarrow \mathbf{2}$

Answer

(D) $\mathbf{P} \rightarrow \mathbf{3 ;} \mathbf{Q} \rightarrow \mathbf{4} ; \mathbf{R} \rightarrow \mathbf{2 ; S} \rightarrow \mathbf{1}$

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Hyperbola

Solution

More JEE Advanced questions on Hyperbola

LIST-I		LIST-II
P.	The length of the conjugate axis of $H$ is	1.	8
Q.	The eccentricity of $H$ is	2.	$\frac{4}{3}$
R.	The distance between the foci of $H$ is	3.	$\frac{2}{3}$
S.	The length of the latus rectum of $H$ is	4.	4