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Let L L ' be the latus rectum through th...

Let `L L '` be the latus rectum through the focus of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` and `A '` be the farther vertex. If ` A ' L L '` is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes).

A

`sqrt3`

B

`sqrt3+1`

C

`(sqrt3+1)//sqrt2`

D

`(sqrt3+1)//sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan30^(@)=(b^(2))/(a+ae)`
`"or "(1+e)/(sqrt3)=e^(2)-1`
`"or "e-1=(1)/(sqrt3)`
`"or "e=(sqrt3+1)/(sqrt3)`
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CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
  1. If the vertex of a hyperbola bisects the distance between its center ...

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

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

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

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

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  6. lf the eccentricity of the hyperbola x^2 - y^2 sec^2 alpha=5 is sqrt3...

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

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  8. Factorise the expression: (x^2–2xy+y^2)–z^2

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

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

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

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

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  13. 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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  14. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

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  15. The number of roots of the equation x^2+5x+6=0 is

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  16. The locus of a point whose chord of contact with respect to the circle...

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  17. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

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  18. The number of possible tangents which can be drawn to the curve 4x^2-9...

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  19. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

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  20. Locus of the feet of the perpendiculars drawn from either foci on a va...

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