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The equation (x^(2))/(12-k)+(y^(2))/(8-k...

The equation `(x^(2))/(12-k)+(y^(2))/(8-k)=1` represents

A

a hyperbola if `klt8`

B

an ellipse if `kgt8`

C

a hyperbola if `8ltklt12`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-HYPERBOLA-QUESTION BANK
  1. Equation of the chord of the hyperbola 25 x^(2)-16 y^(2)=400, which is...

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  2. The equation of a tangent parallel to y=x drawn to (x^(2))/(3)-(y^(2))...

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  3. The equation (x^(2))/(12-k)+(y^(2))/(8-k)=1 represents

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  4. The equation to the normal to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1...

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  5. The line 3 x+4 y+5=0 is a tangent to the hyperbola x^(2)-4 y^(2)=5 at

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  6. The centre of the hyperbola 2 x^(2)+5 x y+3 y^(2)+3 x+4 y+9=0 is

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  7. The asymptotes of a hyperbola are the coordinate axes. If the hyperbol...

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  8. The distance between the directrices of the hyperbola x^(2)-y^(2)=4 is

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  9. If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in f...

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  10. 2x +sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of cont...

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  11. If a hyperbola passes through a focus of the ellipse (x^(2))/(25)+(y^(...

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  12. If (5,12) and (-9,12) are the foci of the hyperbola passing through th...

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  13. Let P(a sec theta,b tan theta) and Q(a sec varphi, b tan varphi) where...

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

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  15. The latus rectum through one focus subtends a right angle at the fart...

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  16. S(1) and S(2) are the foci of an ellipse and B is the end of the minor...

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  17. If the pair of lines b^(2) x^(2)-a^(2) y^(2)=0 are inclined at an angl...

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  18. The distance between foci of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is 9 an...

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  19. The length of the transverse axid , along x - axis with centre at orig...

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  20. The eccentricity of the hyperbola whose latus rectum is 8 and conjugat...

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