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Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where...

Let `H :(x^2)/(a^2)-(y^2)/(b^2)=1` , where `a > b >0` , be a hyperbola in the `x y` -plane whose conjugate axis `L M` subtends an angle of `60o` at one of its vertices `N` . Let the area of the triangle `L M N` be `4sqrt(3)` . LIST-I LIST-II P. The length of the conjugate axis of `H` is 1. `8` Q. The eccentricity of `H` is 2. `(sqrt(4))/3` R. The distance between the foci of `H` is 3. `2/(sqrt(3))` S. The length of the latus rectum of `H` is 4. `4` The correct option is `P->4;\ \ Q->2;\ \ R->1;\ \ S->3` (b) `P->4;\ \ Q->3;\ \ R->1;\ \ S->2` (c) `P->4;\ \ Q->1;\ \ R->3;\ \ S->2` (d) `P->3;\ \ Q->4;\ \ R->2;\ \ S->1`

A

`Prarr4,Qrarr2,Rrarr1,Srarr3`

B

`Prarr4,Qrarr2,Rrarr1,Srarr2`

C

`Prarr4,Qrarr1,Rrarr3,Srarr2`

D

`Prarr3,Qrarr4,Rrarr2,Srarr1`

Text Solution

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B
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Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where a gtb gt0 , be a hyperbola in the x y -plane whose conjugate axis L M subtends an angle of 60o at one of its vertices N . Let the area of the triangle L M N be 4sqrt(3) . LIST-I LIST-II P. The length of the conjugate axis of H is 1. 8 Q. The eccentricity of H is 2. (sqrt(4))/3 R. The distance between the foci of H is 3. 2/(sqrt(3)) S. The length of the latus rectum of H is 4. 4 The correct option is Prarr4;\ \ Qrarr2;\ \ Rrarr1;\ \ Srarr3 (b) Prarr4;\ \ Qrarr3;\ \ Rrarr1;\ \ Srarr2 (c) Prarr4;\ \ Qrarr1;\ \ Rrarr3;\ \ Srarr2 (d) Prarr3;\ \ Qrarr4;\ \ Rrarr2;\ \ Srarr1

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MOTION-HYPERBOLA-EXERCISE-4 (Level-II)
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  5. A hyperbola, having the transverse axis of length 2 sin theta, is conf...

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  6. Match the statements in Column I with the properties in Column II. A

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  7. Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by...

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  9. Match the conics in column I with statements/ex- pressions in Column I...

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  10. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

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  11. The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 in...

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  12. The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 intersect at the...

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  13. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

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  14. Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=...

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  15. Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1If t...

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  16. Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x2,0) ...

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  17. Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where a > b >0 , be a hyperbola in ...

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