Home
Class 12
MATHS
The eccentricity of the conjugate hyperb...

The eccentricity of the conjugate hyperbola of the hyperbola `x^2-3y^2=1` is (a) 2 (b) `2sqrt(3)` (c) 4 (d) `4/5`

A

2

B

`2//sqrt3`

C

4

D

`4//5`

Text Solution

Verified by Experts

The correct Answer is:
A
The given hyperbola is
`(x^(2))/(1)-(y^(2))/(1//3)=1`
Its eccentricity e is given by
`(1)/(3)=1(e^(2)-1)`
Hence, eccentricity e' of the hyperbola is given by
`1=(1)/(3)(e'^(2)-1)`
`"or "e'^(2)=4`
`"or "e'=2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWERS TYPE|18 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMOREHENSION TYPE|21 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.6|4 Videos

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

The eccentricity of the hyperbola 4x^(2)-9y^(2) =36 is:

Which of the following can be slope of tangent to the hyperbola 4x^2-y^2=4? (a) 1 (b) -3 (c) 2 (d) -3/2

Knowledge Check

  • The eccentricity of the hyperbola x^2-y^2=4 is

    A
    2
    B
    `2sqrt2`
    C
    `sqrt2`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    Find the coordinates of the foci and the center of the hyperbola, x^2-3y^2-4x=8

    Find the eccentricity of the hyperbola with asymptotes 3x+4y=2 and 4x-3y=2 .

    The eccentricity of the hyperbola 9x^(2) -4y^(2) + 36 = 0 is

    The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the vertex A lies on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the side B C must touch parabola (b) circle hyperbola (d) ellipse

    If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

    Let P(x, y) is a variable point such that |sqrt((x-1)^2+(y-2)^2)-sqrt((x-5)^2+(y-5)^2)|=3 , which represents hyperbola. The eccentricity e' of the corresponding conjugate hyperbola is (A) 5/3 (B) 4/3 (C) 5/4 (D) 3/sqrt7

    Find the ratio of the eccentricities of the hyperbolas 2x^(2) - 3y^(2) = 1 and 3x^(2) - 2y^(2) = 1

    Home
    Profile