Home
Class 11
MATHS
If the distance between the foci of a hy...

If the distance between the foci of a hyperbola is `16` and its eccentricity is `sqrt(2)` , then obtain its equation.

A

`x^(2) - y^(2) = 32 `

B

`(x^(2))/(4) - (y^(2))/(9) = 1`

C

`2x^(2) - 3y^(2) = 7 `

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS (FILL IN THE BLANKS)|10 Videos
  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS (TRUE/FALSE QUESTIONS)|5 Videos
  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE 11 (H) (LONG ANSWER TYPE QUESTIONS I )|6 Videos
  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos
  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

The distance between foci of a hyperbola is 16 and its eccentricity is sqrt2 , then the equation of hyperbola is

The distance between the foci of a hyperbola is 16 and its eccentricity is sqrt(2) then equation of the hyperbola is x^(2)+y^(2)=32b.x^(2)-y^(2)=16c*x^(2)+y^(2)=16dx^(2)-y^(2)=32

Find the standard equation of hyperbola in each of the following cases: (i) Distance between the foci of hyperbola is 16 and its eccentricity is sqrt2. (ii) Vertices of hyperbola are (pm4,0) and foci of hyperbola are (pm6,0) . (iii) Foci of hyperbola are (0,pmsqrt(10)) and it passes through the point (2,3). (iv) Distance of one of the vertices of hyperbola from the foci are 3 and 1.

If the distance between the foci of a hyperbola with x-axis as the major axis is 16 units and its eccentricity is (4)/(3) , then its equation is

If distance between foci of an ellipse equals its latus-rectrum , then its eccentricity is

Statement- 1 : If the foci of a hyperbola are at (4,1) and (-6,1) and eccentricity is (5)/(4) , then the length of its transverse axis is 4 . Statement- 2 : Distance between the foci of a hyperbola is equal to the product of its eccentricity and length of the transverse axis.

If length of the transverse axis of a hyperbola is 8 and its eccentricity is sqrt(5)//2 then the length of a latus rectum of the hyperbola is

If the distance between the foci of an ellipse is equal to length of minor axis, then its eccentricity is

MODERN PUBLICATION-CONIC SECTIONS -OBJECTIVE TYPE QUESTIONS (MULTIPLE CHOICE QUESTIONS )
  1. The equation of the ellipse whose centre is at origin and which passes...

    Text Solution

    |

  2. The eccentricity of the hyperbola whose latuscrectum is 8 and conjugat...

    Text Solution

    |

  3. If the distance between the foci of a hyperbola is 16 and its eccen...

    Text Solution

    |

  4. The length of the transverse axis of a hyperbola is 7 and it passes th...

    Text Solution

    |

  5. Equation of the hyperbola with eccentricity 3/2 and foci at (±2,0) is

    Text Solution

    |

  6. The equation of the chord joining the points (x(1) , y(1)) and (x(2), ...

    Text Solution

    |

  7. The foci of the hyperbola (x^(2))/(16) -(y^(2))/(9) = 1 is :

    Text Solution

    |

  8. Centre of the circle 2x^(2) + 2y^(2) -x = 0 is :

    Text Solution

    |

  9. For the circle x^(2) + y^(2) = 25, the point (-2.5, 3.5) lies :

    Text Solution

    |

  10. (i) Centre of the circle x^(2) + y^(2) - 8x + 10 y + 12 = 0 is Cen...

    Text Solution

    |

  11. Length of the semi-latus -rectum of parabola : x^(2) = -16y is :

    Text Solution

    |

  12. The focus of the parabola y^(2) = - 4ax is :

    Text Solution

    |

  13. The length of latus-rectum of parabola x^(2) = - 16 y is :

    Text Solution

    |

  14. The eccentricity of the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) = 1 ...

    Text Solution

    |

  15. If the slope of the line containg the point (2,5) and (x, - 4) is 3, t...

    Text Solution

    |

  16. If the slope of a line is not defined then the line :

    Text Solution

    |

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

    Text Solution

    |

  18. The foci of the ellipse (x^(2))/(4) +(y^(2))/(25) = 1 are :

    Text Solution

    |

  19. The co-ordinates of the foci of the ellipse 9x^(2) + 4y^(2) = 36 are ...

    Text Solution

    |

  20. If e and e' be the eccentricities of two conics S=0 and S'=0 and if e^...

    Text Solution

    |