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If x^(2)/(12-k) -(y^(2))/(k-8)=1 represe...

If `x^(2)/(12-k) -(y^(2))/(k-8)=1` represents a hyperbola then

A

`k lt 8`

B

`k gt 12`

C

`8 lt k lt 12`

D

`k= pm 12, k = +8`

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The correct Answer is:
C
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AAKASH SERIES-HYPERBOLA-Practice Exercise
  1. Match the numerical difference of the focal distance of any point on t...

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  2. Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e...

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  3. If x^(2)/(12-k) -(y^(2))/(k-8)=1 represents a hyperbola then

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  4. The vertices of the hyperbola ((x-2)^(2))/( 9) -((y-3)^(2))/( 4) =1 a...

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  5. The equation of the latusrecta of the hyperola ((x-4)^(2))/(16)-((y-3)...

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  6. The length of the conjugate axis of the hyperbola 9x^(2) -16y^(2) - 1...

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  7. The length of the latus rectum of the hyperbola 25x^(2)-16y^(2)=400 is

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  8. The foci of the hyperbola 9x^(2) -16y ^(2)+18x +32 y- 151=0 are

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  9. The length of the latus rectum of the hyperbola 9x^(2) -16y^(2) +72x ...

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  10. The equation of directrices of the hyperbola 5x^(2) -4y^(2) -30x -8y ...

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  11. The equations of the latus recta of the hyperbola 9x^(2) -16y^(2) -18...

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  12. If sec theta is the eccentricity of a hyper bola then the eccentricity...

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  13. The eccentricity of the hyperbola 9x^(2) -16y^(2) =144 is

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  14. If the latusrectum subtends a right angle at the centre of the hyperbo...

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  15. The eccentricity of the hyperola whose latus rectum subtends a right a...

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  16. z=x+iy is a conplex number. If the imaginary part of z^(2) is 32. then...

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  17. In the line 3x-y= k is a tangent to the hyperbola 3x^(2) -y^(2) =3 ...

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  18. If the line x Cos alpha+y Sin alpha=p touches x^(2)/a^(2)-y^(2)/b^(2)=...

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  19. The equations of the tangents to the hyperbola 2x^(2) -3y^(2) =6 whic...

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  20. The number of tangents to x^(2)//25-y^(2)//9=1 through (5,0) is

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