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If a,b are eccentricities of a hyperbola...

If a,b are eccentricities of a hyperbola and its conjugate hyperbola then `a^(-2)+b^(-2)=`

A

4

B

1

C

`a^(2)b^(2)`

D

`a^(-2)b^(2)`

Text Solution

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The correct Answer is:
C
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Assertion (A): The pair of asymtotes of x^(2)/(10)-y^(2)/4=1 and the pair of asymptotes of x^(2)/(10)-y^(2)/4=-1 coincide. Reason (R) : A hyperbola and its conjugate hyperbola posses the same pair of asymptotes. The correct answer is

AAKASH SERIES-HYPERBOLA-Exercise -I
  1. The equation of the latusrectum of the hyperbola 3y^(2)-4x^(2)=12 are

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  2. The equation of the axes of the hyperbola 9x^(2) -16y^(2) +72x -32y -1...

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  3. If a,b are eccentricities of a hyperbola and its conjugate hyperbola t...

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  4. The eccentricity of the conjugate hyperbola of the hyperola x^(2)-3y^(...

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  5. If e(1) and e(2) are eccentricities of the hyperbolas xy=c^(2) and x^2...

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  6. The locus of the point ( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2)) is a h...

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  7. The distance between the foci is 4sqrt(13) and the length of conjugate...

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  8. The latus rectum of a hyperbola (x^(2))/( 16) -(y^(2))/( p) =1 is 4(1...

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  9. If the latus rectum through one focum subtends a right angle at the fa...

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  10. If the lactus recturm of a hyperbola through one focus subtends 60^@ a...

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  11. If the latus rectum of a hyperola forms an equilateral triangle with t...

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  12. The line y=mx+2 touches the hyperola 4x^(2)-9y^(2)=36 then m=

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  13. Equations of tangents to the hyperbola 4x^(2)-3y^(2)=24 which makes an...

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  14. The equation of the tangents to the hyperbola 3x^(2) -4y^(2) =12 whic...

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  15. The point of contact of 9x+8y-11=0 to the hyperbola 3x^(2)-4y^(2)=11 i...

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  16. The nummber of tangents to x^(2)//9-y^(2)//4=1 throught (6,2) is

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  17. For all real values of m' the straight line y=mx + sqrt(9m^(2)-4) is a...

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  18. The condition that the line x=my+c may be a tangent of x^(2)/a^(2)-y^(...

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  19. Product of perpendiculars from the foci of x^(2)/4-y^(2)/9=1" to "y=mx...

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  20. If m1, m2, are slopes of the tangens to the hyperbola x^(2)//25-y^(2)/...

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