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Tangents drawn from ` (alpha , beta ) ` to the hyperbola ` x^(2) //a^(2) -y^(2)//b^(2) =1 `make angles ` theta _1 and theta _2` with the axis .If ` tan theta _1 tan theta _2=1 then alpha ^(2) -beta ^(2) =`

A

` a^(2) `

B

` b^(2)`

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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DIPTI PUBLICATION ( AP EAMET)-Hyperbola -EXERCISE 1A
  1. Tangents to the hyperbola x^(2)//a^(2) -y^(2)//b^(2)= 1 make angle th...

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  2. Tangents to x^(2) //a^(2) -y^(2)//b^(2) =1 make angles theta1 ,thet...

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  3. Tangents drawn from (alpha , beta ) to the hyperbola x^(2) //a^(2) ...

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  4. The locus of the point of intersection of tangents to the hyperbola x^...

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  5. A line through the origin meets the circle x^(2) +y^(2) =a^(2) at P ...

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  6. The product of the perpendicular from the foci on any tangent to the h...

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  7. From any point on the hyperbola x^(2) -y^(2) =a^(2) -b^(2) two tange...

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  8. The equations to the common tangents to the two hyperbolas x^(2)//a^(2...

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  9. The equation of the common tangents drawn to the curves y^(2) =8x and...

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  10. The length of the straight line x-3y =1 intercept by the hyperbola x...

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  11. The product of the perpendicular from the foci on any tangent to the h...

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  12. The equation to the pair of asymptotes of the hyperbola 2x^(2) -y^(2)...

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  13. The equations of the asymptotes of the hyperbola 4x^(2) -9y^(2) =36 a...

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  14. The angle between the asymptotes of the hyperbola x^(2) -3y^(2) =3 i...

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  15. The angles between the asymptotes of the hyperbola x^(2)//a^(2) -y^(2...

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  16. The angles between asymptotes of the hyperbola xy =c^(2) is

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  17. The asymptotes of a rectangular hyperbola intersect at an angle

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  18. The combined equation of the asymptotes of the hyperbola xy+x+y+5=0 is

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  19. The asymptotes of the hyperbola 6x^(2) +13xy +6y^(2) -7x -8y-26 =0 ar...

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  20. The equation to the hyperbola with vertex (4,0) and having asymptotes ...

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