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 reciprocal to that of the ellipse `x^(2) + 4y^(2) = 4`. If the hyperbola passes through a focus of the ellipse, then

A

the hyperbola has the equation `x^2/3- y^2/2=1`

B

the focus of the hyperbola is `(2,0)`

C

the eccentricity of the hyperbola is `(2,0)`

D

the hyperbola has the equation `x^2 - 3y^2 =3`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Recap of Facts and Formulae

    A DAS GUPTA|Exercise Exercise|9 Videos

  • Screening Tests

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

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

Eccentricity of the hyperbola x^(2) - y^(2) = a^(2) is :

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

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

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

The eccentricity of the hyperbola (sqrt(2006))/(4) (x^(2) - y^(2))= 1 is

The eccentricity of the hyperbola 5x ^(2) -4y ^(2) + 20x + 8y =4 is

A DAS GUPTA-Recent IIT questions-Exercise
  1. Let (x0,y0) be the solution of the following equations (2x)^(In2)=(3...

    Text Solution

    |

  2. Q. Let P={theta:sin theta-cos theta=sqrt2 cos theta} and Q={theta:sin ...

    Text Solution

    |

  3. Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec ...

    Text Solution

    |

  4. Let alpha and beta be the roots of equation x^2-6x -2=0. If a...

    Text Solution

    |

  5. A straight line L through the point (3,-2) is inclined at an angle 60^...

    Text Solution

    |

  6. Let the straight line x=b divide the area enclosed by y=(1-x)^2, y=0 a...

    Text Solution

    |

  7. The vector(s) which is/are coplanar with vectors hat(i)+hat(j)+2hat(k)...

    Text Solution

    |

  8. Let the eccentricity of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 b...

    Text Solution

    |

  9. Let Ma n dN be two 3xx3 non singular skew-symmetric matrices such that...

    Text Solution

    |

  10. Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in...

    Text Solution

    |

  11. Let U1 , and U2, be two urns such that U1, contains 3 white and 2 red ...

    Text Solution

    |

  12. Given that the drawn ball from U2 is white, the probability that head ...

    Text Solution

    |

  13. If the point P(a, b, c), with reference to (E), lies on the plane 2x +...

    Text Solution

    |

  14. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  15. Consider the parabola y^(2) = 8x. Let Delta(1) be the area of the tria...

    Text Solution

    |

  16. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))),w h e r e-pi...

    Text Solution

    |

  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  18. The positive integer value of n >3 satisfying the equation 1/(sin(pi/n...

    Text Solution

    |

  19. The minimum value of the sum of real numbers a^(-5),a^(-4),3a^(-3),1,a...

    Text Solution

    |

  20. If z is any complex number satisfying |z-3-2i|le 2 , then the maximum...

    Text Solution

    |