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If the distances of one focus of hyperbo...

If the distances of one focus of hyperbola from its directrices are 5 and 3, then its eccentricity is

A

`sqrt2`

B

2

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`ae-(a)/(e)=3and ae+(a)/(e)=5`
`therefore" "ae=4and (1)/(e)=1`
`therefore" "a^(2)=4`
`therefore" "a=2`
`therefore" "e=2`
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CENGAGE-HYPERBOLA-Exercise (Single)
  1. If a variable line has its intercepts on the coordinate axes ea n de^(...

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  2. A hyperbola, having the transverse axis of length 2sin theta, is conf...

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  3. If the distances of one focus of hyperbola from its directrices are 5 ...

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  4. Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1 be confocal (a > A and a> ...

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  5. Two tangents are drawn from a point on hyperbola x^(2)-y^(2)=5 to the...

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  6. Equation of the rectangular hyperbola whose focus is (1,-1) and the co...

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  7. If two circles (x+4)^(2)+y^(2)=1 and (x-4)^(2)+y^(2)=9 are touched ext...

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  8. If the vertex of a hyperbola bisects the distance between its center ...

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  9. The eccentricity of the hyperbola whose length of the latus rectum is ...

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  10. Let L L ' be the latus rectum through the focus of the hyperbola (x^2)...

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  11. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

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  12. The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 ...

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  13. lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 ti...

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  14. The equation of the transvers and conjugate axes of a hyperbola are, r...

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  15. Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with ve...

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  16. If two points P & Q on the hyperbola ,x^2/a^2-y^2/b^2=1 whose centre i...

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  17. The angle between the lines joining the origin to the points of inters...

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  18. A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), s...

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  19. If the distance between two parallel tangents having slope m drawn to ...

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  20. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

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