Home
Class 12
MATHS
Let the eccentricity of the hyperbola (x...

Let the eccentricity of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` be the reciprocal to that of the ellipse `x^(2)+4y^(2)=4`. If the hyperbola passes through a focus of the ellipse, then the equation of the hyperbola, is

A

the equation of the hyperbola is `x^(2)/3-y^(2)/2=1`

B

a focus of the hyperbola is (2, 0)

C

the eccentricity of the hyperbola is `sqrt5/3`

D

the equation of the hyperbola is `x^(2)-3y^(2)=3`

Text Solution

Verified by Experts

The correct Answer is:
B,D
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    MOTION|Exercise EXERCISE-4 (Level-I)|4 Videos

  • FUNCTION

    MOTION|Exercise Exercise - 4 | Level-II|7 Videos

  • INDEFINITE INTEGRATION

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|6 Videos

Similar Questions

Explore conceptually related problems

Let the eccentricity of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 be reciprocal to that of the ellipse x^(2) + 4y^(2) = 4 . If the hyperbola passes through a focus of the ellipse, then

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

The eccentricity of the hyperbola 3x^(2)-4y^(2)=-12 is

Let the eccentricity of the hyperbola (x ^(2))/(a ^(2))- (y ^(3))/(b ^(2)) =1 be reciprocal to that of the ellipse x ^(2) + 9y ^(2) =9, then the ratio a ^(2) : b ^(2) equals

Find the eccentricity of the hyperbola 9y^(2)-4x^(2)=36

The eccentricity of the hyperbola x ^(2) - y^(2) =25 is

MOTION-HYPERBOLA-EXERCISE-4 (Level-II)
  1. If a hyperbola passes through the focus of the ellipse x^(2)/25+y^(2)/...

    Text Solution

    |

  2. Let ABCD be a square of side length 2 units. C2 is the circle through ...

    Text Solution

    |

  3. Let ABCD be a square of side length 2 units. C(2) is the fircle throug...

    Text Solution

    |

  4. Let ABCD be a square of side length 2 units. C(2) is the circle throug...

    Text Solution

    |

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

    Text Solution

    |

  6. Match the statements in Column I with the properties in Column II. A

    Text Solution

    |

  7. Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by...

    Text Solution

    |

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

    Text Solution

    |

  9. Match the conics in column I with statements/ex- pressions in Column I...

    Text Solution

    |

  10. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  11. The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 in...

    Text Solution

    |

  12. The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 intersect at the...

    Text Solution

    |

  13. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

    Text Solution

    |

  14. Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=...

    Text Solution

    |

  15. Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1If t...

    Text Solution

    |

  16. Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x2,0) ...

    Text Solution

    |

  17. Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where a > b >0 , be a hyperbola in ...

    Text Solution

    |