Home
Class 12
MATHS
An ellipse intersects the hyperbola 2x^(...

An ellipse intersects the hyperbola `2x^(2)-2y^(2)=1` orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

A

equation of the ellipse is `x^2 + 2y^2=2`

B

foci of the ellipse are `(+- 1,0)`

C

equation of the ellipse is `x^2 + 2y^2=4`

D

foci of the ellipse are `(+- sqrt 2,0)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

Similar Questions

Explore conceptually related problems

An elllipse intersects the hyperbola 2x^(2) - 2y^(2) =1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes and the equation of the ellipse is x^(2) + ky^(2) =k then the value of k is ______ .

An ellipse intersects the hyperbola 2x^2-2y =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (b) the foci of ellipse are (+-1, 0) (a) equation of ellipse is x^2+ 2y^2 =2 (d) the foci of ellipse are (t 2, 0) (c) equation of ellipse is (x^2 2y)

The eccentricity of the ellipse ax ^(2) + by ^(2) + 2 fx + 2gy + c =0 if axis of ellipse parallel to x -

" In an ellipse the major and minor axes are in the ratio " 5:3 " The eccentricity of the ellipse is "

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

Intersection of Ellipse with Hyperbola

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 DAS GUPTA-Objective Tests-Exercise
  1. In a triangle ABC with fixed base BC, the vertex A moves such that cos...

    Text Solution

    |

  2. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

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

    Text Solution

    |

  4. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  5. For the function f(x)=x "cos" 1/x, x ge1

    Text Solution

    |

  6. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  7. The area of the region bounded by the curve y=e^(x) and lines x=0 and ...

    Text Solution

    |

  8. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  9. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

    Text Solution

    |

  10. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

    Text Solution

    |

  11. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  12. If the angle A , B and C of a triangle are in arithmetic progession an...

    Text Solution

    |

  13. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |

  14. The equation of the plane containing the straight line x/2=y/3=z/4 and...

    Text Solution

    |

  15. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  16. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  17. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  18. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  19. A signal which can be green or red with probability 4/5 and 1/5 respec...

    Text Solution

    |

  20. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

    Text Solution

    |