Hyperbola question

2018 · Shift 2 · Q35

Hyperbola question

2018 · Shift 2 · Q35

Let

H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1

, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60

^\circ

at one of its vertices N. Let the area of the

\Delta

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.	${4 \over {\sqrt 3 }}$
R.	The distance between the foci of H is	3.	${2 \over {\sqrt 3 }}$
S.	The length of the latus rectum of H is	4.	4

A
P $\to$ 4 ; Q $\to$ 2 ; R $\to$ 1 ; S $\to$ 3
B
P $\to$ 4 ; Q $\to$ 3 ; R $\to$ 1 ; S $\to$ 2
C
P $\to$ 4 ; Q $\to$ 1 ; R $\to$ 3 ; S $\to$ 2
D
P $\to$ 3 ; Q $\to$ 4 ; R $\to$ 2 ; S $\to$ 1

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Hyperbola question

2018 · Shift 2 · Q35

Hyperbola question

2018 · Shift 2 · Q35

Let

H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1

, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60

^\circ

at one of its vertices N. Let the area of the

\Delta

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.	${4 \over {\sqrt 3 }}$
R.	The distance between the foci of H is	3.	${2 \over {\sqrt 3 }}$
S.	The length of the latus rectum of H is	4.	4

A
P $\to$ 4 ; Q $\to$ 2 ; R $\to$ 1 ; S $\to$ 3
B
P $\to$ 4 ; Q $\to$ 3 ; R $\to$ 1 ; S $\to$ 2
C
P $\to$ 4 ; Q $\to$ 1 ; R $\to$ 3 ; S $\to$ 2
D
P $\to$ 3 ; Q $\to$ 4 ; R $\to$ 2 ; S $\to$ 1